Let X be a random variable with the probability distribution below. Find E(X) and E (x²) and then, using these values, evaluate E[(3x + 2)²]. X f(x) Find E(X). E(X)= t - 3 3 6 1 2 9 1 6

Q: Albert and Billy are playing a dice game, but not with the usual dice. Albert's die has one "6" and…

A: We have given that  Albert's die has one "6" and five "4's" while Billy's die has two "5's" and four…

Q: Find the expected value of each probability mass function.

A: Given: x P(x) 0 0.05 1 0.13 2 0.31 3 0.3 4 0.07

Q: If X is a random variable with probability distribution shown below, find E(X). x Pr[X-x] -2 0.1 0…

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Q: E and F are mutually exclusive events. P(E) = 0.1; P(F) = 0.6. Find P(E | F).

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Q: If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine…

A: Given: The probability generating function of a random variable X is given as:…

Q: Let X be a random variable with probability distribution as shown below: -1<x<2 f (x)={3 and…

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Q: 1<x < 3 | f(x) = {C(x - 1)(3 – x) diğer

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Q: Determine the value c so that each of the following functions can serve as a probability…

A: a) It is needed to find the value of c.

Q: x 0  1 2 3 P( X= x ) 0 k 2k 3k Show that k= 1/6. Find the mean of the probability distribution and…

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Q: Determine f(2)  using the indicated probability distribution of the discrete random variable X…

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Q: p(z) $(z) 0.5 .69146 2.0 97725 1.0 |.84134 2.5 .99379 1.5 .93319 3.0 .99865 7. Find each…

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Q: Consider the probability distributions shown here. X=x -4 -3 -2 |-1|01 2 3 4 p(x) 0,02 0,07 0,1 0,15…

A: The following table shows the provided outputs of the discrete random variables, along with the…

Q: Let x be a Poisson random variables. Find the probabilities for x using the Poisson Form

A: Given that X be a Poisson random variable with parameter μ=2.5. The probability mass function for X…

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: The plot to the right shows the probability function of a random variable Z. Estimate the needed…

A: For the given plot Find P ( z &gt;=3 or z =-1 ) = ? P ( z &gt;=3 ) +P(  z =-1 ) = P( z = 3 ) + P( Z…

Q: Let F(z) be the cumulative distribution function (cdf) of a random variable X. Which of the…

A: Based on the property of cumulative distribution, P(a&lt;X&lt;b) = F(b) - F(a) F(a) + P(a&lt;X&lt;b)…

Q: Биррose X1, Xz,. ,Xn be i.i.d. random variables with X; ~ exp(A). Find the distribution of E" X; and…

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Q: Let X be a random variable with the following probability values. f(x) = c(1 – 2x2 + x³), x = 0,1,…

A: Let X be a random variable with the following probability values. fx=c1-2x2+x3,    x=0,1,2,3,4,5 a)…

Q: Find the probability distribution for Y. The table for the probability distribution of Y may have…

A: Here, Y = X^2 + 1

Q: The random variable X has probability distribution given in the table below -2 -1 1 2 P(X=x) 0.1 0.3…

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Q: Let X denote the number of hours you study during a randomly selected school day. The probability…

A: Let X denotes the no. of hours you study during a randomly selected school dayP(X=x)=

Q: 1. Find the value of c. 2. Find the expectation E[X] of X. 3. Find the variance Var(X) of X. (c,…

A: The provided information is as follows:The  is a random variable with the probability density…

Q: Consider a random variable X with the following probability function: 0.3 if x = 0, 0.2 if æ = 1,…

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Q: The probability distribution of random variable X is defined as follows:   X 0 1 2 3 4…

A: The expected value is calculated by the product of each observation and the corresponding…

Q: Solve for P(X < 4). Express your answer in two (2) decimal places. P(X s 4) =

A: Given : X 1 2 3 4 5 6 p ( X )  0.12 0.09 k 0.08 0.11 0.33

Q: Compute P(X) using the binomial probability formula. Then determine whether the normal distribution…

A: Given: n = 42 p = 0.6 q = 1-p = 1-0.6 = 0.4 q = 0.4 Formula Used: Probability mass function of…

Q: Please answer the two problem separately and refer to its instructions. Thank you. Problem 1: (I…

A: Given information: μ=3.2, σ=0.92

Q: Let X have a binomial distribution with parameters n and p. If E(x)=10, Vare(X)=6, then n=

A: given  for binomial distribution E(x)=10=npVar(x) =6=npq

Q: Q: Let X and Y be random variables such that E[X] = 2 and E[Y] = 3 . a. Find E[4X + 5Y] . b. Find…

A: It is given that E(X)=2 and E(Y)=3.

Q: Given that b>a, determine the value of k that results in the following function being a probability…

A: Following conditions should be met for the distribution to be probability distribution.

Q: Let the probability distribution function of X be defined as follows. (0.6+x x =0,1,2,3 10 S(x)={…

A: Here, we have

Q: 9. Let the probability distribution function of X be defined by: = { a ()", x= 0, 1, 2, 3, 0, p(x)…

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Q: 2. Let the joint probability function of X and Y be given by (x+ x) if x 0, 1, 2 and y = 1, 2 p(x,…

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Q: Let X be a random variable with the probability distribution below. Find g(x), where g(x) = (2x +…

A: Given datax          -3        6         9f(x)       512      112      12andg(x)=(2x+3)2

Q: Let X be a random variable with the following probability distribution. Value  x  of  X P(X=x) -2…

A: Given, X P(X=x) -2 0.25 -1 0.20 0 0.40 1 0.10 2 0.05

Q: Let the probability function of the random variable X be f(x) = {  x/45 if x = 1, 2, 3, ⋯ ⋯ ,9…

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Q: X is a discrete random variable with the probability distribution function: k Pr[X = k] 4 1 12 2 2…

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Q: Derive the value of k that minimizes the expectation E[(X-k)²], where X is a random variable.

A: The objective is to minimize the expectation, EX-k2, where X is a random variable. For optimizing…