Probability and Statistics

Board: JEE Advanced |Exam:JEEAdvanced

JEEAdvancedstudynotesforProbabilityandStatisticsbyAjayYadav.In-depthcoverageofadvancedtopicsandproblem-solvingtechniques.

KeyConcepts

Probability

Conditionalprobability,Bayestheorem,independentevents.Probabilitydistributions.Expectation,variance.Binomial,Poisson,Normaldistributions.

Statistics

Mean,median,modeforgroupeddata.Meandeviation,standarddeviation,variance.Coefficientofvariation.Skewness,kurtosis.

RandomVariables

Jointdistributions.Conditionalexpectation.Covariance.Correlationcoefficient.Linearregression.

ImportantFormulas

Binomialmean	np
Binomialvariance	npq
Poissonmean	λ
Poissonvariance	λ

SolvedExamples

Example1:Acoinbiased:P(H)=2P(T).Tossedtwice.FindP(atleastoneH).

Solution:LetP(T)=p,P(H)=2p,3p=1,p=1/3.P(H)=2/3.P(atleastoneH)=1-P(bothT)=1-(1/3)(1/3)=8/9.

PracticeQuestions

1. Twodicetossed.FindP(sum=7|first die shows 3).
2. A random variable has P(X=k)=ck for k=1,2,3,4. Find c.
3. In Poisson distribution, P(X=0)=e⁻². Find λ and P(X=1).
4. Find mean and variance of binomial with n=10, p=0.2.
5. Events A and B have P(A)=0.5, P(B)=0.4, P(A∩B)=0.1. Find P(A|B) and P(B|A).

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