Let X be a discrete random variable with probability function as shown in the following table. x -2 -1 0 1 2 f(x)=P(X=x) 1/8 a b 1/8 1/8 calculate p(|X-1|<2)

Q: Let X be a Poisson random variable such that P(X=1)=P(X=2). Compute P(X=0). l'information est…

A: We have given that,  X be a Poisson random variable with,  P(X=1) = P(X= 2)  Then,  We will find…

Q: 2. The discrete random variable X has the probability function kx, x = 2,4, 6 P(X = x) = - 2), x = 8…

A: From the given information, it is clear that,  The discrete random variable X has a probability…

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: (b) Let a discrete random variable X have the following PMF: p(x) = k (=) , for x = 1,2, . ..; 0,…

A: Basic probability

Q: Let X be a discrete random variable with the cumulative distribution function: 0 if x < 1 if 1<x<3…

A: Given X is a discrete random variable with cumulative distribution function:  F(x) = 0           if…

Q: Let X and Y be two discrete random variables with a joint probability distriībution given by X-2 X-3…

A:

Q: Let X be a discrete random variable with probability function f(x) = kx for x = 0,2,5,7. The value…

A:

Q: 3) The joint probability function of two discrete random variables X and Y is given by f(x; y) =c(2x…

A: Given discrete random variables X and Yf(x,y) = c(2x + y) where 0 ≤ x ≤ 2; 0≤ y ≤ 3, f(x,y) = 0…

Q: Let X be a discrete random variable with probability mass function in the form х 1 2 3 4 5 f(x) 0.1…

A: Let X be a discrete random variable with probability mass function.

Q: Theorem 4. Let X be a discrete random variable with probability function p(x), g1(X), g2(X), g3(X),…

A:

Q: Let X be a random variable with E (X") = 0.8 for n = 1,2,3, . , 00 the moment generating function of…

A: Given: X be a random variable with EXn=0.8  for all  n=1,2,3.....∞ we need to find the Moment…

Q: Let X be a random variable with p.d.f f(x) = c+ 1.2x2,0<x< 1. Find a constant c if E(X) = ! 0.6 0.4…

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Q: 2. Let X and Y are two discrete random variables with joint probability function as follows: Values…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: b) Let Y, and Y, be discrete random variables with a joint probability distribution as shown in the…

A: Given: The joint probability distribution of the random variable Y1 and Y2 is provided as:…

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

A: Correct answer is  0.7

Q: Let X be a discrete random variable with the following probability density function -3 -2 P(X=x)…

A: Solution

Q: Let x be a random variable with probability density function p(x) - 0.4(0.6)*-1 x= 1,2,3,.. %3D %3D…

A: The probability density function is  p(x)=0.40.6x-1                       x=1,2,3,....

Q: Let X1 ~ N(0, 1), X2 ~ N(0, 1), and X3 ~ x²(n) be mutally independent random variables. Find the…

A: a) If X1, X2,…., Xn are mutually independent normal random variables with mean µ1, µ2,…., µn and…

Q: Let X be a random variable with probability distribution as shown below: if x<0 f(x) = { 1 e 5.6 5.6…

A:

Q: 15 - The random variable X takes the values 0, 1, and 2 with probabilities 1/4, 2/4 and 1/4,…

A: Correct answer is (A) 0

Q: A probability distribution is given. -1 POO 0.2 0.3 0.5 Find caf. Xs-1 0.2 -12 Xs-1 0.2 -12 x<-1 0.2…

A: The cumulative distribution function is on the real number line and it is a non decreasing function…

Q: Example 8 : A random variable X gives measurements x between 0 and 1 with a 12x - 21x2 +10x, for 0…

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Q: For the discrete random variable X, P(X = 1) = p = 1 – P(X = -1). Please find c so as to be E(cX) =…

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

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Q: 1) Let the probability function of a discrete random variable X be 100) = {(²+²) (0.5) (05) 1-²,…

A: Solution

Q: (a) Let X1 and X2 be independent random variables having geometric distribution p(x) = q*p; x = 0,…

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Q: Let X be the discrete random variable with the probability function f (x) = kx³ + 0.15 %3D for x =…

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Q: For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =

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Q: 6. A discrete random variable X has a cumulative distribution function, f as follows. 0, 3c, 2sx<4…

A: The probability distribution is fx=0,    x&lt;23c,   2≤x&lt;45c,   4≤x&lt;67c,   6≤x&lt;81,  x≥8…

Q: Let X be a random variable such that E(X – 2)² = 10 and E(X+ 1)² = 4, then 1 а. Е(X) = - b. E(X) = =…

A: How to obtain E(X) 1. Simplify both expression to get two equation 2. Simplify both equation and…

Q: The random variable X is defined as X N (50,100). Calculate the probability P (45 <X <= 87047944…

A: Given, The random variable X is defined as X~N(50,100). X~Nμ,σ2=N50,100 σ=σ2=100=10

Q: Let X be a discrete random variable with probability function f(x) = kx for x = 0,2,5,7. The value…

A: Use the condition of valid pdf to find the value of k, i.e.∑x=07f(x)=1

Q: 0. Let X be a non-negative discrete random variable. Prove that E(X) = | (1-F(2)) dæ 0,

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Q: 17 For a discrete random variable X if: * A (2 Points) P(X = x) = 0.Lx ,x = 2, 3, 5, then E (X²) = O…

A: INTRODUCTION  EXPECTATION :  The expected value of a discrete random variable is a weighted average…

Q: For a discrete random variable X if: * (2 Points) P (X = x) = 0.1x ,x = 2, 3, 5, then E (X²) = %3D…

A: Correct answer is 3.8

Q: Let X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6)…

A: The following information has been given: We have given that X is a discrete random variable. P(X =…

Q: 1) Let the probability function of a discrete random variable X be >= {(²9) f(x) = (0.5)*(0.5)16-x,…

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Q: Let X1, X2, andX3 be independent and normally distributed random variables with E(X1) = 4, E(X2) =…

A:

Q: Let X be a discrete random variable with P(X = -1) = .3, P(X = 1) = .45, P(X = 2) = .15 and P(X = 6)…

A: The following information has been given: We have given that X is a discrete random variable.  P(X =…

Q: X is a discrete random variable with the probability distribution function: x Pr[X = x] -4 29 8 -3…

A: Sum of all probabilities =1

Q: Theorem 4. Let X be a discrete random variable with probability function p(x), 91(X), 92(X), g3(X),…

A:

Q: Theorem 4. Let X be a discrete random variable with probability function p(x), g1(X), 92(X), g3(X),…

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Q: Let X be a discrete random variable with probability function f(x) = kx for x = 1,2,3,4. The value…

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Q: A discrete random variable Y has the probability function as given below. Y -2 2 4 P(Y) 0.25 0.50…

A: In the given table  We have  P( -2)= 0.25 P(2)= 0.50 P(4)= 0.25 As per the rule of probability…

Q: A- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x=…

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Q: 4. Let X1 and X2 be discrete random variables with the joint multinomial distirbution x2 2-x1-x2 2…

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Q: If P(X=-1)=5P(X=0), calculate P(X=0)

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Q: The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4, 6…

A: Given: The probability function is, PX=x=kx,x=2,4,6k(x-2),x=80otherwise The objective is, To prove…

Q: Let X be a discrete random variable with probability function f(x) = c(x2 +3)for x=0, 1, 2 and 3.…

A:

Q: If X is a Poisson random variable with parameter 2, then O a. f(x,A) = . -, x = 0,1,2,... Ob. E(X)…

A: 9. Identify the correct option. The correct option is identified below: Poisson distribution:   The…