2. Let X be a binomial random variable with E(X) = 30 and Var(X) = 21. Find the parameters n and p of X.

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

Q: Let X be a random variable such that E(X²) a. V(3x-3) b. E(3x-3) = 58 and V(X) = 40. Compute

A:

Q: f x is a binomial random variable, find p (x) for n = 6, x = 3, p = 0.5.

A: Solution: Let X has binomial random variable with parameter n= 6 and p= 0.3 X~B(n=6,p=0.5) The…

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: A random variable X can take only the values 2,5 , and 3. It is known that Pr[X= 2] = 0.1 and…

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Q: 2. Suppose that X is a random variable with E(X) = 6 and Var(X) = 4. Find the following: a) Е(4X +…

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Q: et X denote a beroulli random variable, that is P(X=1) =p and P(X=0)=1-p and let Y be a binomial…

A: Given information X~Ber(p) and Y~Bin(n,p)

Q: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

Q: For events A and B we have P(A) = 0.3, P(B) = a and P(AUB) = 0.7. Then the value of a if A and 4. B…

A: Note: " Since you have asked multiple questions, we will solve the first question for you. If you…

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

A: Given,E(X)=2Var(X)=4we know that…

Q: Suppose that X and Y are random variables with E(XY)=E(X)E(Y). The. X and Y (Must be/ cannot be/ may…

A: E(XY)=E(X)E(Y)

Q: Suppose that the random variable X satisfies P(X=a) = p and P(X=b) = 1-p, where a<b. Verify that…

A:

Q: Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X).

A:

Q: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 find the mean and variance of…

A: Let x1,...x40 be IID binomial random variable with parameters p = 0.3 We need to find the mean and…

Q: Let X(n,p) denote a binomial random variable with parameters n and p. Show that X(n+1,p)>=st X(n,p).

A: Given To prove that

Q: If 'b' is Constant and X be a Random Variable then VX +b)3V(X)

A:

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: 40% of the fruit flies posses certain gene. So, probability that a fruit fly posses that gene = 0.4…

Q: Suppose a and b be two possible values of a random variable X with a > b The probability that lies…

A: Given that a and b be two possible values of a random variable X with a &gt; b The probability that…

Q: Let x be a binomial random variable with n = 5, x = 3 and p = 0.75; find P (3) using the binomial…

A:

Q: A grade in a probability course depends on exam scores X1 and X2. The professor, a fan of…

A: As per guidelines of Bartleby,we are giving here solution of first 3 parts only.

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: The Mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. Find A and B, both greater…

A: Given that X follows Normal(mean=5, SD=3) Then Z=(X-mean)/SD= (X-5)/3 follows standard normal…

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: Let X be a random variable such that a. V(3x-3) b. E(3x-3) E(X²) = 58 and V(X) = 40. Compute

A: Answer:- Given, X be a random variable such that  E(X2) = 58 and V(X) = 40               (a) Find…

Q: show all solution 1. Suppose X is a random variable with E(X2)=10 and E(X)=2. Find the following:…

A: Variance of constant is 0.

Q: Let X be a binomial random variable with parameters n = 20 and p ( p is intentionally not given in…

A: From the provided information, Sample size (n) = 20 Since the value of p is not provided therefore,…

Q: Let x be a binomial random variable with n = 20 and p = 28 / 100 Find P (2 ≤ x ≤ 4) and P (x > 1).

A: Given: n=20 p=0.28

Q: A binomial random variable X reveals p=100 and o=20. Calculate P{X=101}.

A:

Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that  P(4 &lt; Y &lt; 16) = P(A &lt; X &lt; B) μX=5σX=3μY=-2σY=6

Q: Suppose that X is a N(3,4) random variable and suppose that Y=2X-1. Determine P(Y>8).

A: We have, Let X be the random variable from normal distribution i.e,  N(3, 4) and Y = 2X-1 Then,  We…

Q: Suppose that X is a geometric random variable with parameter π. Show that P(X = n+k|X > n) = P(X =…

A:

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

Q: If the random variable X is distributed through the N ( 20 , 25 ) then P ( X > 30 ) =

A:

Q: If x" bin(n1,p) and x2~bin(n2,p) then find the distribution of x1|x1+x2 ; where x1 and x2 are…

A:

Q: Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X,…

A: Given that the mean of aX+bY is 3  So,  E(aX+bY)=3aE(X)+bE(Y)=3a(1)+b(2)=3a+2b=3a=3-2b ..........(Eq…

Q: If X and Y are independent random variables with X~N(2,32) and Y~N(1,42), find P(X<Y). (You need to…

A:

Q: Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are…

A: The objective of the question is to prove that if X and Y are independent discrete random variables…

Q: Let X be a binomial random variable with parameters of 9 and 0.1. Let Y be a binomial random…

A: Given that X+Y=2 So, the possible pairs are (0,2), (1,1), (2,0) So,…

Q: Let X and Y be any two random variables and let a and b be any two real numbers. Then var(ax + bY) =…

A: We know that ; For any constants  and b ;  Var(aX + bY) = a2V(X) + b2V(Y)+2 ab Cov(X,Y)

Q: 4. Show that if X and Y are independent random variables, then E(9(X)| X = ro) = g(ro). %3D

A: We need show that if X and Y are independent random variables, then E(g(X) | X = xo) = g(xo).

Q: Q1:Show that: If X1, X2, ., X, are independent random variables and X = X1 + X2 +….+ X, , then Q2:…

A: Note: As per bartleby guidelines for more than one questions asked, only one question is to be…