Let X₁ and X₂ be independent random variables. Suppose that X₁ follows a Poisson distribution with parameter X₁, and that X2 follows a Poisson distribution with parameter 2. Let Y = X₁ + X₂. (a) Use the MGF technique to find the distribution of Y. (b) Find E(Y) and Var(Y).

Q: If the number of random sleigh sightings x follows a Poisson distribution with a mean = 1.7, then…

A: Let X follows Poisson distribution with parameter λ=1.7   Poisson distribution:

Q: Define gamma distribution with parameters 5 and 7 and obtain its moment generating function. Hence…

A:

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

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

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: Let x = (x₁,...,xn) be a data set, and denote its sample standard deviation with sx. Let y₁ = ax; +…

A:

Q: a. What is the probability that she is a woman and likes accounting courses? b. What is the…

A:

Q: Hummingbirds visit a feeder at a rate of 0.75 visits per hour.  Let X be the number of hummingbird…

A: Given,Hummingbirds visit a feeder at a rate of 0.75 visits per hourLet X=no.of hummingbird visits on…

Q: Let X1,...,Xn be a random sample from the distribution f(x) = 2x, 0 < x < 1. Find the distribution…

A: f(x)=2x ; 0&lt; x&lt; 1 n be the sample size

Q: X2 are independent continuous random variables with a uniform distribution in the interval (a, b).…

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: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Part (a) Coefficient of correlation ρ(X,Y)The coefficient of correlation ρ  is defined…

Q: d) The random variable X has a Poisson distribution such that P(X= 0) = P(X = 1). Calculate P(X =…

A: Given problem Given that   d)   The random variable X has a Poisson distribution such that P( X=0…

Q: An epidemic process is such that an infected individual is infectious for a time period which is…

A: Here, given that the epidemic process is such that an individual is infectious for a time period…

Q: Let Y denote a random variable that has a Poisson distribution with mean 2 = 4. (Round your answers…

A: We have given that,  Let Y be the random from Poisson distribution with λ = 4 Then,      Note:-…

Q: et X be a discrete random variable with P(X = -2) = .1, P(X = 1) = .15, P(X = 2) = .4, P(X = 4) =…

A:

Q: Let X be a binomial random variable with parameters n and 0₁. Condi- m, let y be a binomial random…

A: Given that X be a binomial random variable with parameters  and .

Q: (6) Let X be a Poisson random variable with parameter 9, then E(X²) = 1.

A: Given X~Pois(θ)

Q: Let X have a Poisson distribution with a mean of 3. Define Y = (X-3) ^2 , specify pdf from Y.

A: Note: According to Bartleby expert guidelines, we can answer only first question with their three…

Q: Let X a b(4,) find Var(3x) and distribution function.

A:

Q: b) Find the variance Var(X) of X.

A:

Q: Let X and Y be random variables with Var(X)=0.64, Var(Y)=0.81, and Cov(X,Y) = 0.5. Find each of the…

A: Step 1: a) It is given that, Var(X) = 0.64, Var(Y) = 0.81 and Cov(X,Y) = 0.5. The coefficient of…

Q: A random variable X has a normal distribution N(4,9). (1) Find V(X) and E(X²). (2) Let + be the cdf…

A: The normal distribution of the random variable is N(4,9).

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: Let X~ N(0, 1) and let Y = -X. (a) Show that Y~ N(0, 1) (by showing that Y has cdf Þ). (b) What is…

A: X follows a standard normal distribution.

Q: Suppose that the random variables X1,...,Xn form a random sample of size n from the uniform…

A: Let X1, X2,.......Xn be the random sample having Uniform distribution (0,1)Y1=min{X1,…

Q: Let X1, X2 and X3 be independent and identically distributed random variables that follow a Poisson…

A: Given:- X1 , X2 , X3 , are independent and identically random variables X1 , X2 , X3  ~ Poisson…

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

A:

Q: 3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probability…

A:

Q: The random variable 'X' has the Poisson distribution Po(m) and P(X=5) = P(X=4) + %3D P(X=3). Find…

A:

Q: he random vector x obtained by adding the vectors x1, x2 and x3 end-to-end has a multivariate…

A: Given: There are three vectors.

Q: 10. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and…

A: The objective of this question is to find the joint and conditional probability density functions of…

Q: Compute the correlation between the random variables Y1 and Y5 = 1+ X1 + X2.

A:

Q: Suppose that X₁, X2, X3 are independent and identically distributed random variables with…

A: Given Cdf  F(x)=1-2-x; x≥0

Q: Suppose that random variable X is uniformly distributed over the interval (0,1). Assume that the…

A: X follows U(0,1) Y|X follows B(n, x)   E(X) = ½ E(Y|X) =nx

Q: E estimator c onal distribut us part, find

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).

A: When X~ Pois(λ) P(X=x)=e-λ λx/x!  ; X=0,1,2,3,.. result: r!=r(r-1)(r-2)..3x2x1

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 =…