Probability Distribution of Bernoulli Trials
T. Dhasaratharaman*
Statistician, Kauvery Hospitals, India
*Correspondence: Tel.: +91 90037 84310; email: dhasa.cst@kauveryhospital.com
A Bernoulli experiment is a random experiment, the outcome of which can be classified in one of two mutually exclusive and exhaustive ways, mainly, Success or Failure (e.g., female or male, life or death, non-defective or defective).
So, it is also called a Binomial trial!
A sequence of Bernoulli trials occurs when a Bernoulli experiment is performed several independent times so that the probability of success, say, p, remains the same from trial to trial. That is, in such a sequence we let p denote the probability of success on each trial. In addition, frequently q=1-p denote the probability of failure; that is, we shall use q and 1-p interchangeably.
Let X be a random variable associated with Bernoulli trial by defining it as follows:
X (success) = 1 and X (failure) = 0. That is the two outcomes, success and failure, is denoted by one and zero, respectively. It can be written as f(x) =px(1-p) 1-x and we say that X has a Bernoulli distribution.
Properties
- A Bernoulli (Success-Failure) experiment is performed n times.
- The trials are independent.
- The probability of success on each trial is a constant p; the probability of failure is q=1-p.
- The random variable X counts the number of successes in the n trials.
A binomial distribution will be denoted by the symbol b(n,p) and we say that the distribution of X is b(n,p). The constants n and p are called the parameters of the binomial distribution, they correspond to the number n of independent trials and the probability p of success on each trial.
A random variable X will have Bernoulli distribution with probability p if its probability distribution is
P(X = x) = px (1 – p)1-x, for x = 0, 1 and P(X = x) = 0 for other values of x.
Here, 0 is failure and 1 is the success.
Example 1: In a hospital, a particular type of operation has 95% chance of success. On a given day, 10 operations were performed. This can be viewed as 10 Bernoulli trials, with each trial having a probability of success p=0.95, and a probability of failure 1-p=0.05.
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Mr. T. Dhasaratharaman
Statistician
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- Journal scan: A review of 25 recent papers of immediate clinical significance, harvested from major international journals
- Recommended Readings
- ஆரோக்கியம் நம் கையில்
- வெற்றியின் பாதை
- Editorial
- Editorial Board
- Prevalence of vitamin D deficiency in a multi-speciality hospital orthopaedic outpatient clinic
- Esomeprazole induced Hypoglycemia
- Dynamic external fixator for unstable intra articular fractures of Proximal Interphalangeal Joint (PIP): “Suzuki” frame
- How to Practice Academic Medicine and Publish from Developing Countries? A Practical Guide, Springer Nature, 2022
- WINTNCON 2022 – Scientific Program
- Pulmonary Thrombo Embolism: A state of the art review
- Role of Artificial Intelligence in improving EHR/EMR and Medical Coding and billing
- Monoclonal Antibodies: Edrecolomab and Abciximab
- Atlas of haematology and hematooncology
- Journal scan
- Learning from Experience – Intra Operative, Chapters 31 and 32
- What doctors must learn: Doctor, look beyond science
- Recommended Readings
- I Whisper Secrets In My Ear
- EDITORIAL
- Instructions for Authors
- Mismatched Haploidentical Bone Marrow Transplantation in a 10-year-old boy with relapsed refractory acute lymphoblastic leukemia, at Trichy
- ST-Segment Elevation is not always Myocardial Infarction
- Acyanotic Congenital Heart Disease, repaired, evolves into a Cyanotic Congenital Heart Disease and presents with an atrial tachycardia
- Family medicine – caring for you for the whole of your life. A Lost and Found Art
- The Principles and Practice of Family Medicine
- Complete Heart Block
- Sick Sinus Syndrome (SSS)
- The First Ever National Award Comes to Kauvery Hospital Chennai & Heart City for Safety and Workforce Category in IMC RBNQA Milestone Merits Recognition 2022
- Diagnostic Image
- PRE-OPERATIVE CHAPTERS 7 AND 7 – LEARNING FROM EXPERIENCE
- Chapter 5: Super-specialist – boon or bane
- Journal scan: A review of 42 recent papers of immediate clinical significance, harvested from major international journals
- RECOMMENDED READINGS
- நேரம் ஒதுக்கு
- மருத்துவரின் மகத்துவம்
- EDITORIAL
- Instructions for Authors
- Surgical Management of Covid-19 Associated Rhino-Orbito-Cerebral-Mucormycosis (Ca-Rocm) – A Single Centre Experience
- Knee Joint Preservation Surgeries
- Guest Editorial Comments
- Ventricular Septal (VSR) closure with ASD device
- Newer Calcium Debulking Angioplasty technique of Orbital Atherectomy
- An hour-long CPR to restart the heart
- VT or SVT with aberrancy?
- Pituitary Neuroendocrine Tumor (PitNET)
- VSD Device Closure
- PDA Device Closure
- Iron Deficiency Anemia, Post MVR
- Torsades de Pointes
- Quality improvement project to Reducing the Malnutrition Rate of ICU patients from 43% to 20%
- Long term use of Amiodarone in Cardiac patients: A Clinical Audit
- Statistical Independent Events and Probability
- PERI-OPERATIVE Chapters 9 and 10 – Learning from Experience
- Journal scan: A review of 40 recent papers of immediate clinical significance, harvested from major international journals
- EDITORIAL
- Kauverian Medical Journal
- First da Vinci Robotic Surgery in Carcinoma Prostate: A Case Report
- Black burden or Taylor the saviour: A case report
- Analysis of differences in Oncology practice between the United Kingdom and India
- A Case of Takayasu Arteritis
- Idiopathic Dilated Pulmonary Artery (IDPA)
- ECG Atlas
- Unusual cause of Dysphagia: A case report
- Tu Youyou: The scientist who discovered artemisinin
- Continuing Nursing Education (CNE) on Risk assessment tools, to assess vulnerable patients at Kauvery Hospital, Tennur
- DIAGNOSTIC IMAGE
- PRE-OPERATIVE CHAPTERS 11 AND 12 – LEARNING FROM EXPERIENCE
- OLD AND NEW – MAKE THE BEST OF THE TWO
- Journal scan: A review of 30 recent papers of immediate clinical significance, harvested from major international journals
- Recommended Readings
- EDITORIAL
- INSTRUCTION TO AUTHORS
- A pregnant patient with DKA, septic shock and a lactate mystery
- Radical Thymectomy in Myasthenia Gravis through Partial Sternotomy approach: A report on three patients
- In-utero blood transfusion in two etiologically distinct anaemic fetus
- RARE CAUSE OF PULMONARY HYPERTENSION
- Acute Rheumatic fever is still an enigma
- A remarkable journey: Managing LQTS in a 43-year-old female with recurrent syncope and seizure
- An unusual case of Acute Coronary Syndrome
- Reversible cause of severe LV Dysfunction in Left Bundle Branch Block
- A case study on Rhino-Orbital-Cerebro- Mucormycosis
- Snakebite and its management
- Total Elbow arthroplasty in Post Traumatic arthritis
- Wellens Syndrome: An ECG finding not to miss!
- Dr. C.R. Rao Wins Top Statistics Award a look back at his pioneering work
- PRE-OPERATIVE Chapters 13 and 14 – Learning from Experience
- Chapter 7. Doctor-patient relationship
- Journal scan: A review of 30 recent papers of immediate clinical significance, harvested from major international journals
- EDITORIAL
- INSTRUCTION TO AUTHORS
- FROZEN ELEPHANT TRUNK (FET) PROCEDURE IN A 52 YEARS OLD CHRONIC AORTIC DISSECTION PATIENT
- DIAGNOSING AND MANAGING EISENMENGER SYNDROME IN A YOUNG MALE
- STEMI EQUIVALENT BUT STEMI!
- TEMPORARY HEAL CAN POSSIBLY KILL!
- UNDERSTANDING PUBERTY
- THE IMPORTANCE OF STATISTICS IN HEALTHCARE
- JOURNAL SCAN: A REVIEW OF 44 RECENT PAPERS OF IMMEDIATE CLINICAL SIGNIFICANCE, HARVESTED FROM MAJOR INTERNATIONAL JOURNALS
- DIAGNOSTIC IMAGE
- PRE-OPERATIVE CHAPTERS 15 AND 16 – LEARNING FROM EXPERIENCE
- CHAPTER 8. DOCTOR-DOCTOR RELATIONSHIP
- EDITORIAL
- GUEST EDITORIAL
- CLINICAL AUDIT: AN INTRODUCTION
- YOUNG ACS AUDIT
- CLINICAL AUDIT: ANAESTHESIA
- CLINICAL OUTCOME IN ICU PATIENTS
- RATE OF MALIGNANCY IN INDETERMINATE OVARIAN CYST – A PROCESS AUDIT
- PATTERNS OF NEEDLE DISPOSAL AMONG INSULIN USING PATIENTS WITH DIABETES MELLITUS: AN AUDIT
- CONTINUOUS PATIENT MONITORING – LIFE SIGNS
- AGE IS JUST A NUMBER!
- SVT WITH LEFT BUNDLE BRANCH BLOCK FOLLOWING GASTRECTOMY
- COMPLEX AORTIC DISSECTION WITH MULTIFACETED CLINICAL PRESENTATIONS
- EDITORIAL
- POST-OPERATIVE SORE THROAT IN GA: A CONCERN
- NEONATAL HLH: OUR EXPERIENCE
- CLINICAL REVIEW MEET 16TH NOV 2023: CHALLENGES IN SETTING UP A NEW HSCT CENTRE IN A TIER-2 CITY IN INDIA
- CARDIAC BIOMARKERS: CLINICAL UTILITY
- HIRAYAMA DISEASE: A CLINICAL-RADIOLOGICAL REVIEW
- ECG AS A WINDOW OF OPPORTUNITY: FOR HYPERKALEMIA
- EFFECTIVENESS OF ROOD’S APPROACH BASED PAEDIATRIC OCCUPATIONAL THERAPY MANAGEMENT: ON CHILDREN WITH CONGENITAL MUSCULAR TORTICOLLIS
- ELTROMBOPAG, A NOVEL THROMBOPOIETIN (TPO) RECEPTOR AGONIST: AN OVERVIEW
- HENOCH-SCHONLEIN PURPURA
- SUBMANDIBULAR GLAND SIALADENITIS SECONDARY TO SUBMANDIBULAR CALCULUS
- LEAN HOSPITALS
- STATISTICS BLACK-SCHOLES MODEL
- PERI-OPERATIVE CHAPTERS 17 AND 18 – LEARNING FROM EXPERIENCE
- CHAPTER 9. BUILDING BLOCKS OF PATIENT CARE
- JOURNAL SCAN: A REVIEW OF 30 RECENT PAPERS OF IMMEDIATE CLINICAL SIGNIFICANCE, HARVESTED FROM MAJOR INTERNATIONAL JOURNALS
- EDITORIAL
- INSTRUCTIONS TO AUTHORS
- ROTATHON-SERIES OF SUCCESSFUL ROTA CASES LAST 2 MONTHS: AN AUDIT
- OUTCOMES OF AKI AUDIT IN KAUVERY
- ETIOLOGY, CLINICAL CHARACTERISTICS AND OUTCOMES OF PATIENTS WITH ACUTE PANCREATITIS IN KAUVERY CANTONMENT HOSPITAL (KCN), TRICHY
- USE OF BLOOD PRODUCTS AND STEROIDS IN THE MANAGEMENT OF DENGUE AT KAUVERY TRICHY HOSPITALS: A CLINICAL AUDIT
- A CLINICAL AUDIT: ON THE MANAGEMENT OF ECTOPIC PREGNANCY
- DIABETIC KETOACIDOSIS WITH HIGH ANION GAP METABOLIC ACIDOSIS
- HYPOKALEMIC PARALYSIS FROM DISTAL RENAL TUBULAR ACIDOSIS (TYPE-1)
- DELAYED PRESENTATION OF INTERMEDIATE SYNDROME IN A PATIENT WITH ORGANOPHOSPHORUS POISONING: A CASE REPORT
- SCAPULA FRACTURES: DO WE NEED TO FIX THEM?
- SPONTANEOUS CSF RHINORRHEA
- DANCING WITH DIABETES: AN UNUSUAL CASE OF CHOREA HYPERGLYCEMIA BASAL GANGLIA SYNDROME
- CONVALESCENT RASH OF DENGUE
- ECG ATLAS 2
- MI MIMICKER
- PERFORATION PERITONITIS-A CASE REPORT
- APPLICATION OF EVIDENCE BASED PRACTICE CARE FOR INDIVIDUALS WITH SPINAL CORD INJURY WITH FUNCTIONAL DIFFICULTIES: ROLE OF THE OCCUPATIONAL THERAPY PRACTICE GUIDELINES
- METHOTREXATE INDUCED MUCOSITIS AND PANCYTOPENIA: A CONSEQUENCE OF MEDICATION ERROR IN A PSORIASIS PATIENT
- POST OPERATIVE CHAPTERS 1 AND 2 – LEARNING FROM EXPERIENCE
- CHAPTER 10. NURTURING SELF
- விடாமுயற்சி வெற்றி தரும்
- JOURNAL SCAN: A REVIEW OF 26 RECENT PAPERS OF IMMEDIATE CLINICAL SIGNIFICANCE, HARVESTED FROM MAJOR INTERNATIONAL JOURNALS
- EDITORIAL
- EDITORIAL BOARD
- LIMB SALVAGE IN EXTREMITY VASCULAR TRAUMA: OUR EXPERIENCE
- MANAGEMENT OF URETHRAL CATHETER RELATED PAIN IN RENAL TRANSPLANT RECIPIENTS: A CLINICAL AUDIT
- NO PAIN VEIN GAIN WITH PRILOX IN PAEDIATRIC POPULATION
- GUIDELINE-DIRECTED MEDICAL TREATMENT (GDMT) OF HEART FAILURE AT KAUVERY HOSPITALS: A CLINICAL AUDIT
- PATIENTS STORY: DIGNITY MATTERS
- PATIENTS STORY: DIGNITY MATTERS
- VIDEO PRESENTATION- CT CORONARY ANGIOGRAPHY
- DRUG INDUCED HYPERKALEMIA
- ADULT NEPHROTIC SYNDROME
- EXPLORING COMPLEX CARDIAC CASES: INSIGHTS FROM DIVERSE PRESENTATIONS IN MID-AGED WOMEN
- EFFECTIVENESS OF ACTIVITY CONFIGURATION APPROACH BASED OCCUPATIONAL THERAPY INTERVENTION FOR CHILDREN WITH CONGENITAL MUSCULAR TORTICOLLIS: A CASE STUDY
- CARDIOMYOPATHY AND ITS ECHO FINDINGS
- THE STRESS TEST ON THE TREADMILL
- POST OPERATIVE CHAPTERS 3 AND 4 – LEARNING FROM EXPERIENCE
- CHAPTER 11. BALANCE IN LIFE BEYOND BANK BALANCES
- JOURNAL SCAN: A REVIEW OF 30 RECENT PAPERS OF IMMEDIATE CLINICAL SIGNIFICANCE, HARVESTED FROM MAJOR INTERNATIONAL JOURNALS
- காணும் பொங்கலும் மனித மன மாற்றமும்
- EDITORIAL
- INSTRUCTIONS TO AUTHORS
- PREVALENCE OF STREPTOCOCCUS PNEUMONIAE SEROTYPES IN AND AROUND TRICHY AND ITS CLINICAL RELEVANCE
- ANAESTHETIC MANAGEMENT OF A PATIENT WITH HUGE GOITER: A CASE REPORT
- EUGLYCEMIC DIABETIC KETOACIDOSIS A RARE CAUSE FOR DELAYED EXTUBATION
- SUCCESSFUL PREGNANCY IN ASD PATIENT – COMPLICATED BY SEVERE PULMONARY ARTERIAL HYPERTENSION
- ENDOCRINE COMPLICATION OF GROWTH HORMONE SECRETING TUMOR: A CASE REPORT
- EFFICACY OF EARLY DIAGNOSIS AND DEVELOPMENT APPROACHES OF PAEDIATRIC OCCUPATIONAL THERAPY ON ACUTE DISSEMINATED ENCEPHALOMYELITIS: A CASE REPORT
- POST OPERATIVE CHAPTERS 5 AND 6 – LEARNING FROM EXPERIENCE
- CHAPTER 12. MILES TO GO – BEFORE TEACHING BECOMES LEARNING
- JOURNAL SCAN: A REVIEW OF 26 RECENT PAPERS OF IMMEDIATE CLINICAL SIGNIFICANCE, HARVESTED FROM MAJOR INTERNATIONAL JOURNALS
- காவேரி – 25
- POEM – மண்ணில் பிறந்தது சாதிப்பதற்குத்தான்