Consider the discrete random variable x with probability distribution p(x). Denote the mean and standard deviation of x as μ and ox, respectively. Now define a new discrete random variable y defined as y = μx - 3x. (a) What is the mean of y, y, in terms of u? (b) What is the standard deviation of y, oy, in terms of ox? (c) Now consider a new random variable z = μx ax, what value of a is the mean of z, z, equal to zero? where a is some constant. For

Q: Let us consider a discrete random variable having the pmf given by, PX(k) = { (1/3) , k = 1   (2/3)…

A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

Q: Calculate the expected value E(X) of the given random variable X. X is the number of tails that come…

A: Given Information: No. of times a coin is tossed/No. of trials (n)=58 P(tail in a coin)=0.5

Q: Let X be a binomial random variable with probability distribution 3-a SOOʻO**, x = 0,1, 2, 3, f(x) =…

A: Solution-: Given: n=3,p=2/5 ∴X→B(n=3,p=2/5) The p.m.f. of X is given by,  P(X=x)=3x*(25)x*(35)3-x…

Q: 7. Calculate the variance of g (X) = 2X + 3, where X is a random variable with probability…

A: The given data is as follows: x0123f(x)

Q: TRY to generalize it for any finite number of independent exponential random variable S. Let Xk -…

A:

Q: Consider the bivariate distribution for the random variables x and y. The expected value of a linear…

A: We want to tell you which one is the correct choice.

Q: (a) A lower bound for P(6<Y <24) (b) the value of k such that P(|Y-15| ≥k) ≤ 0.09.

A:

Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

A:

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

A: We have given that  X and Y are independent random variables with expected values E[X] = 0, E[Y] =…

Q: te random variable. Let E(X)=10 and Var(X)=5. Since Y = x2 + 3X, What is E(Y)=?

A:

Q: -17 Let X₁, X2, and X3 be mutually independent random variables with the following probability…

A: We are given three independent random variables, X1, X2, and X3, with probability density functions…

Q: Let x be a dis crete random variable with probability distribution fCx) =k (x² + 20) and x =…

A: i. From the given information, the probability distribution function is f(x) = K (X2 + 20) and x=…

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

A:

Q: Let X be a random variable with p.d.f f(x) =)",x = 1,2,3,. Find P(A), where A={1,3,5, ..} 2/3 2/5 O…

A:

Q: r= 1, 2, 3, ... Determine the moment generating function and hence mean and the variance. Assume P +…

A:

Q: let Y be a random variable that can either be equal to 0 to 1. let p(Y=1)=p,what is E(|Y-p|)?

A:

Q: We define the ratio random variable of two random variables X and Y is Z = . (a) If X~ Binomial (3,)…

A: Given that the ratio random variable of two random variables X and Y is Z=XY.

Q: Determine the expected value and standard deviation of a random variable Y=2X+100 when X has a pmf…

A: Solution: The probability mass function of random variable X is  x 2 3 4 5 Total  f(x)  0.3 0.3…

Q: A fair 6-sided die is tossed. If X denotes the random variable giving the number on the bottom face…

A: The sample space of 6-sided die tossed is {1,2,3,4,5,6}. It is given that X denotes the random…

Q: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2…

A: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2 +…

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: Let ξ and η be independent standard normal random variables. Find the distribution of X = ξ/η

A:

Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: Pr(Y) 0.5 We know X and Y are independent, so Pr(XIY) = Pr(X) and vice versa, Pr(YIX) = Pr(Y) for…

A: The formula for correlation for X and Y is, CorX,Y=CovX,YVarXVarY Then the formula for covariance…

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

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

A:

Q: -3) = , P(X = 1) = }, P(X = 8) : %3D ot the cumulative distribution function of X. lulnto the values…

A: x y -3  1/8 0  3/4 1 1    Probability mass function: It is a discrete random variable that…

Q: x is a random variable with a mean ux = 70 and variance o*2 = 36 Find the arithmetic scale and…

A: Given that  μx=70 , σx2=36   Variance of constant term is zero

Q: random variable X is normal with mean 2 and standard deviation 2, then what is P(x2 - 4x < 1). 3

A:

Q: Let X be a binomially distributed random variable B(n, p) with E(X) = 2 and Var(X) = 4/3. Find n.

A:

Q: x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the…

A:

Q: what's r and e, both greater than 0 so that  P(4 < T < 16) =P(r< Z < e)

A: Given that Z~ N( mean=5, SD=3) then  P=(Z-mean)/SD= (Z-5)/3 follows standard normal distribution i.e…

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