Let X denote the number of VCRs sold during a random week by a certain store. The probability function of X is f(x) 0 0.1093 1 0.3998 2 0.0823 3 0.2455 4 0.1631 X Calculate the variance of the number of VCRs sold in a random week. Var(X) = 1.9533 X

Q: Let X~N(2,1), Y~N(-1,2). X and Y are independent. Find the probability distribution for Z=X - 2Y.

A: The probability density function of normal variable is given by, f(x)=1σ2πe-12x-μσ2 Given: X~N(2,1)…

Q: a. Calculate the probability that X1 is less than 0.5 and that X2 is between 0.4 and 0.7. b. Show…

A: f(x1,x2)=2(1-x1)   0≤x1,x2≤1   P(0<x1<0.5,0.4<x2<0.7) =∫x1=00.5∫x2=0.40.72(1-x1) dx1…

Q: Suppose Z has the standard normal distribution. Find the cumulative distri- bution function, density…

A: Given information: Z has the standard normal distribution.

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

A:

Q: 10. Let F(x) - cumulative distribution function of the random variable . Find the cumulative…

A: Given that, F(x) is the cumulative distribution function of the random variable ξ.

Q: I. Let X be the number of courses that thirty part-time students were taking this term. The…

A: Given data is  Number of Courses (x) P(x=x) 1 5/10 2 10/30 3 7/30 4 4/30 5 2/30 6…

Q: Let Z be a standard normal random variable. Calculat (a) Pr(-1.3 < Z < 0) (b) Pr(.25 s Z)

A:

Q: For the cumulative distribution function, find a. U b. P(x> 2) c. F(x= 6) d. P(x = 6) e. f(x = 4) f.…

A: The cumulative distribution function of x is given as:

Q: Porphyrin is a pigment in blood and other body fluids that is significant in body energy and…

A: According to the provided information, μ = 38 and σ = 12.

Q: b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

A:

Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

A:

Q: What is the distribution of X? 1) Out of the 38 pizzas that you try, how many would you expect to…

A: Let p be the probability of you liking the pizza. Given that p = 0.08

Q: Let x be a discrete Probability distribution Fi Cand x= -L.0,l,2+3 į Find the value of K i. Find the…

A: Discrete Random Variable  Two numbers are often used to summarize a probability distribution for a…

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: Porphyrin is a pigment in blood and other body fluids that is significant in body energy and…

A: According to the provided information, μ = 38 and σ = 12

Q: Let X be a random variable with mean 6 and variance 3. Let Y be the random variable counting the…

A: Given that  E(X) = 6 , V(X) = 3 Let Y be the random variablecounting the number of times the number…

Q: be able wopue. əui un variance Var(X). Then the standard deviation o x of X is defined by Select…

A: We want to tell Let X be a finite random variable with the variance Var (X). Then the standard…

Q: X,,X2, ... ,X, is a random sample selected from the normal distributionx,~N(6,25) ·Ã and 52 is the…

A: There are nine random variables X1 , X2 ,....., X9 where Xt=N(6,25). The sample mean and sample…

Q: Let X be a random variable having an exponential distribution with parameter equal to 3.3. Find the…

A: given data  exponential distribution λ = 3.3 P(x does not fall in interval 0.3 to 0.4) = ?

Q: From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 5 pieces of…

A: 0.070Explanation:Step 1:  correlation coefficient  between X and Y is given by…

Q: Let X be a binomial random variable with n=7 and p=0.1, then The variance of X is 0.63 P(X>1)=…

A: Given: n=7 and p=0.1 Then, the variance isVariance=np1-p=70.11-0.1=70.10.9=0.63

Q: Suppose X₁ and X₂ have the following joint distribution X₁ 1 d 2 1/3 1/12 1/6 0 2 1/36 0 0 0 X₂ 1 0…

A:

Q: Prove that the E(X) = 1/p for a geometric distribution, where x is the number of trials.

A: The geometric distribution with probability that ranges from 0 to 1 is a discrete probability on the…

Q: Compute the mean and variance of a random variable whose distribution is uniform on the interval [a,…

A: Given: Consider a random variable X following Uniform distribution with the range a and b. The…

Q: Let B is a r.v (random variable) with Bernoulli distributionand parameter p > 0.5 . Let Var(B) =…

A: Given that, B is a random variable with Bernoulli distribution. p&gt;0.5 VarB=0.21 As, B is a…

Q: Let Z be the standard normal random variable. Let X1 = Z, X2 = -Z be independent random variables.…

A: We have given that,  Z from the standard normal distribution with mean = 0 and variance = 1 i.e,…

Q: et X be a random variable with the following probability distribution. Valuex of X P(X=x) -30 -20…

A: let X be a random variable with the following probability distribution.

Q: Let X be the random variable of the normal distribution with mean (u) and standard .deviation (o) If…

A:

Q: Let X be a random variable with a uniform distribution over the interval [-2 , 4].   Determine the…

A:

Q: The marginal distributions of two random variables X and Y, together with some values of their joint…

A: Given  P(X=0)=0.5, P(X=1)=0.3, P(X=2)=0.2 P(Y=1)=0.5, P(Y=3)=0.5  Result: If X and Y are independent…

Q: X is the number of successes in 10 independent Bernoulli trials. The variance of X is equal to 1/4…

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: 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

Q: Let X and Y be independent random variables with the distributions X ∼ Geometric(p = 1/3) and Y ∼…

A: