Let X be a binomial random variable with parameters n and 0₁. Condi- m, let y be a binomial random variable with parameters tional on X -m and 02. = (a) What is the marginal distribution of Y? = (b) Find the functions g(k)= E(Y|X = k) and v(k) = Var(Y|X = k). Use these to find E(Y) and Var(Y). (c) Find Covariance(X, Y) and Correlation (X, Y).

Q: Let X = N(μ, A), where 2 3 -2 1 -0) --(9) -- (₁) and A = -2 20 1 02 Determine the conditional…

A: Let , where and

Q: True or False;  For a continuous random variable X, P(X=x) = f(x) 1. True 2.False

A: In statistics, the continuous variables are variables whose values can be given by an interval, they…

Q: Let Y₁,..., Yn be an iid sample U(0, 0), 0 > 0, with pdf 0≤ y ≤ 0, and CDF f(y) = { 0, elsewhere…

A: Given Yi ~U(0,θ) pdf  f(y)=1/θ 0<y<θ  Cdf  F(y)=y/θ

Q: Find the PSD of a stationary random process for which Auto correlation is RYx (t) 6 e- alt|

A:

Q: Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y…

A:

Q: Q3: let x be random variable with Beta distribution, find the V(x)?

A: Beta Distribution: A continuous random variable X is said to follow Beta distribution with…

Q: p.d.f. f(z;8) = e-(-9) I(0,00) (). Here we use the indicator function of set A defined by IA(2) = 1,…

A:

Q: 6) (13 points) The random variable X has the following probability density function: x 1x(x)=2 0,…

A:

Q: Let X, and X, be independent exponential distributions with the same parameter 1. What is the joint…

A: Given:  X1 & X2 are independent random variables with pdfs             f(x1)=λe-λx1; x1>0…

Q: Find the minimum mean square error forecast A forecast error e, (1) and Varfe, (1)1 for the…

A:

Q: X and Y are two independent random variables with fx (x) = e - u (x) and fy (V) = e. u (y). Find the…

A: Given : fXx = e-x ·uxfYy = e-y ·uyz = x-y

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: Let X and Y be identically distributed with mean 4 and variance 25.(a) If X and Y are uncorrelated,…

A: a) If X and Y are uncorrelated then Cov(X,Y)=0, given V(X)=V(Y)=25 Answer(a): 50

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 continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

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

A:

Q: 5.5.4. Let Y1, Y2, ..., Yn be a random sample from the uniform pdf fy(y; 0) = 1/0, 0 ≤ y ≤ 0.…

A: Step 1: Step 2: Step 3: Step 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: 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: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

A:

Q: If Y is a standard Cauchy random variable, show that Y and are identically distributed. Y

A: Solution

Q: The random variables X and Y represent the number of vehicles that arrive at two separate street…

A: The random variables X and Y represent the number of vehicles that arrive at two separate street…

Q: 2A random variable has a pimif given by olw

A: Solution

Q: Suppose that the conditional distribution of Y given X = x is Poisson with mean E(Y|x) = x, and that…

A: d) From the given information, The conditional distribution of Y given X=x is Poisson distribution…

Q: Let X denote a random variable that has a Poisson distribution with mean 1= 2. Find (a) P(X = 4) %3D…

A: Here X~ Poisson with parameter 2. We need to find the required probabilities.

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: û = ax + by, where a and b are real numbers. Find the expected value of this estimator in terms of a…

A:

Q: The amount of water in a reservoir at the beginning of the day is a random variable X and the amount…

A: The amount of water left in the reservoir at the end of the day: Z= X-Y

Q: Q2/ Let X be a random variable with normal distribution N(0,4) and Y=(X+2)² find:- 1- P(Y > 1) 2-…

A: 2) Given Y=(X+2)2, we want to find the probability that Y is greater than 1 . This is equivalent to…

Q: Random variable X has a standard normal distribution. Find the PDF of the random variable Y, where:…

A: a) To find the probability density function (PDF) of the random variable Y = 3X - 1, where X follows…

Q: 3- 3 f(r) = I = 0,1,2, 3.

A: We have given that  Number of trials n=3 Success of probability p=1/4=0.25 q=1 - p= 1 - 0.25 q=0.75…

Q: Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

A: Solution

Q: Let w₁, W2,..., wt be independent random variables from a normal distribution with mean 0 and…

A: Let w1, w2......wt be independent random variables from a normal distribution with mean 0 and…

Q: Calculate the Average and the variance

A:

Q: Find the value of Var(X − 2Y + 7).

A: It is given that Var(X)=6, Var(Y)=3  and ρ(X, Y)=-14.

Q: Suppose that X is a random variable with distribution function given by I< 1, 1<r< 2, 2 <x < 3, 3<r.…

A: