Let μ and σ2 denote the mean and variance of a random variable X. Determine: (a) E[(X −μ)/σ] (b) E{[(X −μ)/σ]2

Q: IfX is a random variable such that E[X] = 15 and E[X] = 250, use the Chebyshev's inequality* to…

A: Given E(X)=μ=15, E(X2)=250, and we want to lower bound of P(4<X<26)

Q: If X and Y are two independent random variables such that E[X]=2, variance of X = o}, E[Y]= 1, and…

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Q: 6- Find the mean value and standard deviation of the random variable X described by the following…

A: Given See the handwritten solution

Q: Suppose the random variable X has pdf Exp(- (u - 2)²), fx(u) = K 2√2π 0≤u≤ 4, otherwise. where K is…

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Q: (a) Find the expectation E (X) of X. E(X)= (b) Find the variance Var(X) of X. Var (x) =

A: Given: Pmf of X is X P(X=x) -20 0.10 -10 0.05 0 0.40 10 0.10 20 0.30 30 0.05 we…

Q: Suppose that X and Y have the following joint probability function: 3r, if0<y< a<1 0, f(x, y) =…

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Q: Find the E(X) of the random variable X with the following PDF: £x(x)=4410.11(x)+(1.2)(x)+(-+)423)(x)

A: 3 Given density function is, fx=x2I0,1x+12I1,2x+-x2+32I[2,3)x      =x2, 0&lt;x&lt;112,…

Q: Consider the discrete random variable X1, with probability pi X = with probability p2 X2, with…

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Q: (a) Find the expectation E (X) of X. E (x) = 0 %3D (b) Find the variance Var(X) of X.

A: We have to calculate the mean and variance of X for given probability distribution.

Q: Let X1, X2,... be independent Exponential (3) random variables and Z = } E=1 X;. If Mz (t) is the…

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Q: Let X1, X2,..., Xn be independent exponential random variables with mean ið. For example, E(X1) = 0,…

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Q: Let X be a random variable such that E(X) = 3 and E(X') = 13. Use Chebychev's inequality to…

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Q: (a) Find the expectation E (X) of X. E (x) = | %3D (b) Find the variance Var(X) of X.

A: The E(X) is defined as E(X) = ∑x.P(X = x) And variance of X is  V(X) = E(X2) - (E(X))2

Q: Let X1, X2, X3, X4 be independent random variables of size 4 from a gamma distribution with α- 6 and…

A: Given : X1, X2, X3, X4 be independent random variable of size 4 from a gamma…

Q: For a certain random variable X it is known that E[X]=2, Var(X)=3. What E[x']?

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Q: Let X be a random variable with the mean µ and the variance. Show that E|X|=3 and E|X­­2|=13, use…

A: The variance is, VarX=EX2-EX=13-32=13-9=4 The variance of X is 4. For constant k&gt;0, the…

Q: Find the variance and standard deviation of a continuous random variable with the given p.d.f. The…

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Q: b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

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Q: a) Suppose that random variables X₁ and X₂ have exponential distribution with expected value of and…

A: It is given that X1 ~ Exponential(1/2) And X2 follows Exponential(1/3)

Q: a) Find the expectation E (X) of X. E (x) = [] %3D b) Find the variance Var(X) of X. Var(X) Var (X)…

A: Consider the table ,  x P(x) x*P(x) x^2*P(x) 30 0.05 1.5 45 40 0.3 12 480 50 0.1 5 250 60…

Q: Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression…

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Q: Let the random variable X and Y have the joint p.d.f. [12xy(1-x) f(x,y)= 0 Find E[X] and Variance o…

A: Given f(x,y) = 12xy(1-x)    0&lt;x&lt;1     0&lt;y&lt;1

Q: 1. Find the value of c to make f (x) = x = 2, 3, 4 into a valid probability distribution. Enter…

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

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

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Q: 1. For any random variable X for which E(X) and E(X²) are finite, show that Var(X) = E(X²) – [E(X)]²…

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Q: Let x, and x2 be independent random variables with respective means µ = 75 and Hz = 50, and standard…

A: Given that , X1 , X2 are two independent random variables ,                   Mean for X1 is ,    μ1…

Q: p.d.f. h(x) of the random variable x is defined by h(x) =3/(4(1-x²)),-1<x< 1,Calculate the standard…

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Q: 1. Let X be a random variable with probability density function f(x) = {k(4 – x²) -2<x<2 otherwise…

A: #1     X   be a random variable with pdf                      f(x)  = k(4-x2)      -2 &lt; x &lt; 20…

Q: Let X, and X, be independent random variables. Suppose the mean of X, and X2 are 2.5 and 3; and…

A: We have to solve given problem:

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

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Q: prove the below Theorems (mean and variance of each) If Y is an exponential random variable with…

A: Given that

Q: (a) Suppose that X1,..., X, are independent Laplace random variables, and let Y, = X1 + ……+ Xn. Find…

A: a)  E[Yn]=E[X1+X2+....+Xn]          =E[X1]+E[X2]+....+E[Xn]           =0+0+........+0            =0…

Q: 4. Let X be a random variable and c and d two real constants. Without recurring to variance…

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Q: (a) Find the expectation E (X) of X. E (x) = [] (b) Find the variance Var(X) of X. Var(x) = D %3D

A: Here given discrete probability distribution of X

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

Q: #1: Let X1 and X2 be independent and identically distributed to random variable X such that X has…

A: Introduction:Since X1, X2 are independent and identically distributed, the following important…

Q: Suppose that X is a Normal random variable with E(X) = 1 and Var (X) = 1. Define Y =2X + 1. Find P(0…

A: Consider, EY=E2X+1=2EX+1∵EaX+b=aEX+b=2*1+1=3 VarY=Var2X+1=22*VarX∵VaraX+b=a2*VarX=4*1=4 SDY=VarY=4=2

Q: X is a discrete random variable with the following PMF: • P(X = 5.5) = 0.25 • P(X = -2.5) = 0.25 •…

A: Formula to find standard deviation of PMF : σ = ∑( xi-μ)2P(Xi = xi )  Where ,  μ is mean of PMF μ =…

Q: Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Given information: The expectation of the random variable X is E(X) = 0 and P(-3 &lt; X &lt; 2) =…

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

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Q: a) Find the expectation E (X) of X. E(X) = 0 (b) Find the variance VarX) of X. Var(X) = 0

A: Given: x P(x) 0 0.35 10 0.35 20 0.05 30 0.25 Total 1

Q: Consider a random variable X taking the values k1, k2, ·.. , kn E R with probability P1, P2, ; Pn E…

A: Formula is

Q: Let X1,... Xn be independent random variables, all having the same distribution with expected value…

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Q: Let X and Y be jointly normal random variables with X, Y ~ N(0, 1) and correlation . Evaluate E [ex…

A: Given :-

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…

A: Given data: Suppose that X is a Poisson random variable with (λ) = 0.02 and t = 50. To Find a. P(X ≥…

Q: X is an exponential random variable with parameter λ = 1/4 Calculate P {X ≤ 4}

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

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Q: 2. Let the random variables Y,, Y2, .., ¥½ be normally distributed with mean 10 and variance 4. Find…

A: Chi-square distribution: Let us assume x1, x2, ... , xn be n independent standard normal variables.…

Q: Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X.…

A: Given information:Given that the mean and variance of the variable X is 3 and 2.That is, E(X) = 3…