Suppose that we have a discrete random variable Xa with PDF and CDF fa(x) and Fa(x), and a continuous random variable X. with PDF and CDF f.(x) and F.(x). Now we create a new random variable X in the following way. We have a coin with P(H) = p. We toss the coin once. If it lands heads, then the value of X is determined according to the probability distribution of X4. If the coin lands tails, the value of X is determined according to the probability distribution of Xe. This is called Mixed Random Variable formulation. Find E[X²].

Q: 1. Suppose that Z, and Z, are discrete random variables with joint probability distribution given in…

A: Z1 and Z2 are independent if p(z1,z2)= p(z1)*p(z2)  Marginal p.d.f of Z1 and Z2 :    Eg:  P(Z1=-1,…

Q: 9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution…

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Q: Let X be a binomial random variable with parameter n and p. Show that E 1- (1– P)"+1 (n + 1)p Lx +…

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Q: Suppose N is a Poisson random variable with mean A. Show that E (1+ for any constant a. +a)^

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Q: Let X be a random variable with p.d.f. 3e-3x f(x) = { 0 <x<00 , find E(x) O.w

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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Q: Consider a random variable X whose cumulative distribution function (cdf) is given by 0 , if x 3 X…

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Q: a.b.c

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A: Given,f(w)=c(w+5);  -5≤w≤70;  otherwise

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Q: Let xbe a Geometric random variable with p%3= 0.6. Find the mgf at zero MO)

A:

Q: Let X and Y be two discrete random variables with a joint probability distribution given by X-0 X-2…

A: P(X&gt;0 and Y&lt;=3) = P(X=2,4 and Y=1,3) =0.02+0.2+0.1+0.1 =0.42 (ans)

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A: Given Data:   x=0 x=2 x=4 y=1 0.03 0.02 0.1 y=3 0.15 0.2 0.1 y=5 0.20 0.15 0.05

Q: 3. Let X1, X2, X3 be a random sample drawn from an exponentially distributed popu- lation with…

A: Solution

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Q: 1. Suppose that Z, and Z2 are discrete random variables with joint probability distribution given in…

A: Z1 and Z2 are independent iff  f(Z1,Z2)=f(Z1)f(Z2)

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A: Solution: From the given information, the probability mass function of X is

Q: 5. Suppose that X is a Poisson random variable with = 0.02 and t = 50. Find a. P(X > 2), b. P(1 < X…

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Q: 1. For every given probability distribution, solve for the variance. a. 1 2 3 P(X) 0.08 0.21 0.23…

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A: It is given that Y=aX+b.

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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.