Suppose a random variable X is claimed to have the cumulative distribution func- tion (CDF) F(r) = 0, x € (0, 0x) IE (-00,0) Show that F(x) is a legitimate CDF.

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A: Basic formula for variance and expectation are used in the given solution

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A: Var[x] = E[x2] - (E[x])2  ========================

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Q: A continuous random variable has a p.d.f. ſkx³(1 – x)²0 < x < 1 | f(x) = Ootherwise

A: Given,f(x)={kx3(1-x)2  ;0&lt;x&lt;10                   ;otherwise

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Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

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Q: A continuous random variable X has the distribution function F(x) = 0 if x 3 The value of k is

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Q: (a) Show that the random variable (2/0) E X, has a x2-distribution with 2n degrees of freedom.

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Q: a. If X is a Poisson variate such that 2P(X=0)=P(X=2),find the probability that P(XS3).

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Q: Probability and statistics

A: a.Computing the expected value of X:The expected value of X is given below:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.