If X is A discrete random variable and f(x) is the probability of X, then the expected value of this random variable is equal to: Ο a Σx+f{x)] O b. Ef(x) O c. Ef(x)+x O d. none of the above

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: 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 discrete random variable with the following pmf k = -2 5 k= -1 k = 0 P(X = k) = * k-1 1…

A: Solution: Define  Y=(X+1)2 The plug the values of X=--2,-1,0,1,2, inY=(X+1)2 the new values of Y is…

Q: If a random variable X is defined such that: E[(X – 2)²] = 18 and E[(X+1)²] = 33. Then the values of…

A: Given: E( (X - 2 ) 2 )= 18 E( (X + 1 ) 2 )= 33

Q: Y:PVI ZV. OA aill Asiacell 1/3 أحصاء امثلة.pdf Out come H. H=1/2 HH=1/4 H=1/2 -H T=1/2 T. HT=1/4…

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Q: Let X be a discrete random variable with probability function as shown in the following table.   x…

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Q: Suppose that the joint probability for random variables X and Y defined by f(x, y) y 1 2 1 28 28 28…

A: Solution: From the given information, the joint probability for X and Y is

Q: Let X be a discrete random variable with probability function as shown in the following table. x -2…

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Q: Suppose X and Y are jointly continuous random variables, the conditional expectation of u(x), given…

A: The conditional expectation of u(x) given y is:

Q: B. Let X and Y be random variables and let A e B. Prove that the function

A: SOLUTION ;

Q: Let X be a binomial random variable with parameter n and p. Show that E 1- (1– P)"+1 (n + 1)p Lx +…

A: there are various method we can use to prove by definition of expectation probability generating…

Q: Let X be a random variable with p.d.f. 0<x<0 S(x) = • ,find E(e3) O.w

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: Let X be a random variable with probability distribution as shown below: 2 <x< 10 f(x) = 3x and g(X)…

A: The E(g(X)) is calculated as E(g(X)) = E(10X + 5) = 10.E(X) + 5

Q: (iii) If X and Y are two discrete random variables, then E(X + Y) = E(X) + E(Y) provided E(X) and…

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Q: The non-negative integer-valued discrete random variable XX has the following probability generating…

A: Given the non-negative integer-valued discrete random variable X has the following probability…

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 expected…

A: Given pdf of random variable is defined by h(x). We have to find the expected value of X that is…

Q: Prove that if M(t) is the MGF of a random variable X, then the MGF of a + bX is e^at M (bt)

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Q: If a random variable X is defined such that: E[(X – 3)²] = 18 and E[(X – 1)²] = 34. Then the values…

A:

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

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Q: Let X be a random variable with p.d.f. 2e-2x 0<x<00 f (x) =• , find E(e 2*) O.w

A: Given, the probability distribution function of a random variable X- fx=2e-2x  ; 0&lt;x&lt;∞0…

Q: If the p. d. f of a random variable X is f(x) = 1,0 ≤ x ≤ 2, then P(X> 1.5|X > 1) is

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Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

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 expected…

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Q: X be the random Variable with the following probability distribution: X: 3 6 9 Р(X): 1/6 1/2 1/3 (d)…

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

A: For a continuous random variable X, the probability density function(PDF) is denoted by fXx and it…

Q: Suppose that X is an exponentially distributed random variable with A = 0.75. Find each of the…

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Q: If øx(@) is a characteristic function of a random variable X, then , (co) = 6, (@), where c is a…

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Q: Suppose X and Y are jointly continuous random variables, the conditional expectation of v(y), given…

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Q: Let X1, X2, ..., X144 be independent identically distributed (i.i.d.) random variables, each with…

A: Let be independent identically distributed random variables each with expectation The standard…

Q: For a random variable X, (E(X))² can be greater than E(X²).

A: We have to find statement is true or false.

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: If a random variable X is defined such that: E[(X – 2)*] = 18 and E[(X +1)*] = 33. Then the values…

A:

Q: Let X be a random variable with p.d.f. ((k +4)(x+2) f (x) ={ 0<x<2 , find (1) k (2) E(x) O.W

A: (a) We know, ∫fx dx=1∫02k+4x+2 dx=1∫02kx+2k+4x+8 dx=1kx22+2kx+2x2+8x02=12k+4k+8+16=16k=-23k=-236

Q: Let X be a continuous random variable with probability distribution as shown below: (x*(2x +), ifo…

A: We need to find expectation of given function

Q: 9. Consider the formula: P(x) = x/21, x 0, 1, 2, 4. Is P(x) a probability mass function? If so, show…

A: 9. The given formula is Px=x221,x=0,1,2,4.

Q: Q2) The joint probability function of two discrete random variables X and Y is given by Ax,y) =…

A: We are given the joint PMF of two discrete random variables X and Y.  f(x,y) = c(2x + y) , for x =…

Q: Denote by { 1* 0 <x<1 0.5 2< x <c . elsewhere f(x) = Find the value of c, such that f(x) is the…

A: Solution: From the given information,

Q: If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+ 1)'] = 33. Then the values…

A:

Q: If a random variable X is defined such that: E[(X – 3)²] = 18 and E[(X+1)²] = 34. Then the values of…

A: The given expectations are EX-32=18 and EX+12=34. Now, EX2+9-6X=18EX2+E9-E6X=18EX2+9-6μ=18EX2-6μ=9…

Q: . Xand Y are random variables, and f(') is the corresponding probability function. Which of the…

A: We need to use the concept of correlation and verify options.

Q: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

A: The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X…

Q: a) Find the value of the constant c

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

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

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Q: If X and Y are two independent random variables, such that E (X) = 17; var (X = o; E (Y) = i rar ()…

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Q: Suppose that X and Y have the following joint probability function: f(x, y) 4 0.15 0.10 0.20 0.10 1…

A: We want to find the expected value of E(XY2) and E(X) and E(Y)

Q: A random variable X has the following probability mass function table X 0 1 2 probability 0.25 0.5…

A: Solution: From the given information, the probability mass function of X is