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RD Sharma Class 12 Chapter 32 Solutions (Mean And Variance Of A Random Variable)

RD Sharma Class 12 Maths Solutions Chapter 32 Mean and Variance of a Random Variable discusses the chapter of Mean and Variance of a Random Variable in detail. The topics you’ll learn here are discrete random variable, probability distribution, mean of a discrete random variable, the variance of a discrete random variable, etc. This chapter helps you to apply all your mathematical concepts learnt previously and solve the questions from CBSE and entrance examinations.

RD Sharma Class 12 Maths Solutions Chapter 32 comprises 2 exercises and a total of 42 questions. You’ll get questions such as determining the probability distribution of a random variable, finding the value of a variable if for a given random variable the probability distribution is given, or finding the probability distribution of the number of aces, and a lot more.

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Some Topics Discussed in RD Sharma Class 12 Maths Solutions Chapter 32 Mean and Variance of a Random Variable

Discrete Random Variable

Consider S = sample space. S is associated with a random experiment that is already given to you. 

Consider X = a real valued function.

This X is now assigned to all the events w ϵ S where X(w) can be known as a random variable.

You can say a random variable as a real-valued function with domain S, the sample space that is associated with the random experiment.

Probability Distribution

Consider a random experiment where you toss three coins simultaneously (or you can say that a coin is tossed three times. Defining the random variable, X on the sample space

S = {HHH, HTH, THH, HHT, THT, TTH, HTT, TTT}

such that X(w) will be the heads in w ϵ S.

 It is evident that X assumes the values = 0, 1, 2, 3

Now, P(X=0) = Probability of getting no head will be = P(TTT) = (⅛)

P(X=1) = Probability of getting one head will be = P(HTT or THT or TTH) = (⅜)

Similarly P(X=2) = Probability of getting two heads will be = P(HTH or THH or HHT) = (⅜)

andP(X = 3) = Probability of getting three heads will be = P(HHH) = (⅛)

Therefore, if a random variable say X has values x1, x2, x3, …, xn and respective probabilities p1, p2, …, pn, then

     X:  x1   x2 x3…. xn

P(X):  p1 p2   p3.… pn

This will be known as the probability distribution of X.

This tabular description where you get the random variable and its values alongside corresponding probabilities will be known as a probability distribution.

The variance of a discrete random variable

Consider X a discrete random variable and it assumes the values x1, x2, x3, …, xn having the probabilities p1, p2, p3, …, on then the X’s variance will be denoted by

Var(X) = E(X2) – {E(X)}2

Discussion of exercise in RD Sharma Class 12 Maths Solutions Chapter 32

  1. The first exercise 32.1 contains 27 questions where some of the questions will talk about finding the probability distribution of a given random variable, finding the value of a variable in P(X) for all values of X, finding the probability distribution of occurrence of aces, finding the probability distribution of a number of heads as the three coins are tossed, determining the probability distribution of X which is a random variable and represents the number of hearts in all the three cards that are drawn, etc.
  2. The second exercise of Mean and Variance of a Random Variable, 32.2 has 15 questions where you will be required to answer questions such as finding the mean and variance of the heads when a coin is tossed three times, find the mean and standard deviation of a number of kings when drawing two cards simultaneously from a deck of cards, finding the probability distribution, variance and mean of X where X is the number that appears twice when a fair die is being tossed, etc.

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