Consider a random variable X taking the values k1, k2, ·.. , kn E R with probability P1, P2, ; Pn E [0, 1] respectively, where pi + P2 + + Pn 1. Write down the formula for the ... expected value of f(X) for a given function f(-).

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A:

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Q: Find fQ|X (q|x) for x ∈ {0, 1} and all q.

A: It is a fact of statistics. It is widely used.

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Q: If X is a random variable with probability density function 32 f (x) = for x = 0, 1, 2, 3, 4 and 5,…

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A: Here given cumulative distribution function of x

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Q: for r, y > 0, f(x, y) = (1+x)2.(1+xy)² > 0, otherwise. Show that X and X Y are independent,…

A: *answer:

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A: a). Find the cdf F(x) of X and sketch the graph: The probability mass function is given below: X…

Q: Let the probability function of the random variable X be defined as f(x)=cx(1-x) for 0<x<1,…

A: f(x) = c(x-x2)   a)We know that, ∫abf(x)dx = 1 ∫01c(x-x2)dx = 1 c(x22-x33)]01 = 1 c(12-13) = 1 c = 6…

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Q: Suppose that the random variable X has the probability density function flW) = 0 ( (1- x²) for - 1s…

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A: Given, f(x)=cx2x-1                   x=2,3,4

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Q: , Let X1, X2, ,X, be a sequence of i.i.d. Bernoulli(p) random variables and let Y, = E X/n. Show…

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Q: Suppose the discrete random variable X has probability function 1. px(1) I = 1,2, 3, I(I +1)"

A: Given  :    pxx  =1xx+1,  x=1,2,3,...

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Q: (a) Show that for any non-negative random variable X, we have E(X)= P(X > t)dt (b) Let the CDF of X…

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Q: If X is a uniform random variable over the interval (8, 12), find E[X]

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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 .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: Suppose x is a normally distributed for continuous random variable with 4-10 and 6. Find value of xo…

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Q: Suppose that a sequence of mutually independent and identically distributed discrete random…

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Q: (52) Let X be a random variable with p.d.f. 1 0<x<0 f(x) = ,find E(e") O.w -in

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Q: Let Z be a N(0, 1) random variable, and let F(x) be thecumulative distribution function for Z. Show…

A: Hello, Thanks for posting your question.  I believe, while writing your question here, you forgot to…

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Q: Let X be a random variable with u = 4 and o = .5. (a) Use the Chebychev inequality to estimate Pr(3…

A: Chebyshev’s theorem: When the distribution of the population is not known. That is, when there is no…

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Q: Suppose X1, X2,..., X10 are independent random variables, Find P(X1+ X2 +...+ X10 < 25), assuming…

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Q: Suppose that the random variable X has the probability density function ´c(1– x²) for -1s x s1 f(x)…

A: f(x)=c(1-x2)     ;  -1≤x≤10                ;  otherwise

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Q: Let X1,..., X10 be a random sample of size 10 from a N(u, o²) population. Suppose 10 E(x; - 4)² Y ||…

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Q: a) Find the value of the constant c

A: The joint pdf is given by f(x,y) = c(2x+y)

Q: (4) Let X be a discrete random variable with domain D. Prove that Var(X) = E(X?) – E(X).

A:

Q: b. Let X and Y be discrete random variables with joint probability function, f as follows, Y = 0 Y =…

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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.