Let X1, X2, ..., X50 be 50 independent and identically distributed exponential random variables with expected value 2. (i) Compute P (X¡ < 3) (ii) Compute P (E, 10X; < 30) i=1 (iii) Compute P((X1 < 3) n (X2 < 3) n ... n (X50 > 3)) (iv) Let Y = 3e'X, + 4X¡. Find E(Y).

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A: Expectation of a Random Variable: The expectation of a random variable X, denoted by E(X), is…

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Q: (6) Let X be a Poisson random variable with parameter 0, then E(X²) = 1. От OF

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Q: Q2/(a) Let X be a random variable with p.d.f. 1<x<o S(x) = { find k. o.w (b) Let X be a random…

A: For the p.d.f to be valid, ∫1∞kx-2dx=1⇒k∫1∞x-2dx=1⇒k-1x1∞=1⇒k-1∞+11=1⇒k(0+1)=1⇒k=1

Q: 1 V(X) for i) X ~ U{1,n}, ii) X~ Geometric (p), iii) X P

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Q: Determine the expected value of g(x,y) = (X^3)+(Y^2)

A: Solution

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Q: Let X be a Poisson random variable with parameter k. (a) Show that the moment generating function…

A: Here X~ Poi(k). Then, P(X=x)=e-kkxx!,x=0,1,2,...0,otherwise a.)The Moment Generating Function of X…

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Q: Suppose X and Y are independent random variables with expected values E[X] = 0, E[Y] = 0, and Var(X)…

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Q: 5. Let X and Y be independent random variables such that X - exp(A) and Y ~ exp(). (a) What is the…

A: It is an important part of statistics. It is widely used.

Q: (6) Let X be a Poisson random variable with parameter 9, then E(X²) = 1.

A: Given X~Pois(θ)

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Q: Q2/(a) Let X be a random variable with p.d.f. kx 1<x<∞ S(x)=• find k. O.w

A: The p.d.f of X is given below: fx=kx-2   1&lt;x&lt;∞0          ow

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A: Here , we have given a pmf which is describes in the question.

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A: Range(x) = Max(x) - Min(x) First we need to find the PDFs of max(X) and min(X).

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A: Range is equal to maximum value minus minimum value

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Q: find k.

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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.