Suppose X has the geometric pmf fx(x) = ()*, z = probability distribution of Y = X/(X+1). Note that here both X and Y are discrete random variables. To specify the probability distribution of Y, specify its pmf. 0, 1, 2,.... Determine the

Q: Let Y1, Y2, ... , Yn be a random sample of size n from a gamma distribution with parameters α = 1…

A:

Q: X is a discrete random variable and takes the values 0,1 and 2 with probabilities of 1/6, 1/3 and…

A: Moment generating function:

Q: Suppose X, Y are two discrete random variables with probability function given by: Y X-1 1/8 1/8 1/8…

A: Multiplication of marginal probabilities are are compared with joint pmf.

Q: Let X be a random variable having the binomial distribution with size n and probability p E (0,1).…

A:

Q: Suppose X is a discrete random variable with finite first and second moments. Show that E (x…

A: It is given that X is a discrete random variable with finite first and second moment.

Q: Let A be a random variable with unified distribution between -2, 2 (A~U[-2,2] ) and b is a constant.…

A:

Q: 9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution…

A:

Q: Let X and Y be two exponentially distributed and independent random variables with mean a and p.…

A: Introduction :

Q: If X is an exponential random variable with parameter 1, and c > 0, show cX is expor

A:

Q: Suppose that X and Y are random variables where the conditional expected value of Y given X is given…

A:

Q: 1. X is a discrete random variable with probability distribution fCe) =(e,x=t, 2,.. ノ otherwise Find…

A:

Q: Find the characteristic function of a uniformly distributed random variable X in the range [0,1] and…

A:

Q: Suppose that Z is a discrete random variable with Var(Z) = 1/2 and E(Z) = 2. Match up the following…

A: 1] Var(Z)=12 2] E(Z)=2

Q: Given p1 and p2 be positive real numbers less than 1 and let X and Y be discrete random variables…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(Probability…

Q: Let X be a random variable with distribution function F(x) = 1-e*,x > 0, then the p.d.f of X is

A: Here given cumulative distribution function of x

Q: Suppose that Y is a continuous random variable. Show EY = yfr(y)dy.

A: Here, we have to prove EY=∫-∞∞yfydy.

Q: 2. Let us consider a discrete random variable having the pmf given by, k = 1 Px(k) = {2 k = 2. 3' 0,…

A: We have been given the pmf as,   Px(k)=13,      k=123,      k=20,        k=3 The mgf is given by,…

Q: Suppose that five random variables X1,·.., X5 are i.i.d., and each has a standard normal distribu…

A: It is given that Xi has a standard normal distribution. The sum of two independent normal variables…

Q: X is an exponential random variable with parameter λ = 4   Calculate P {X ≤ 3

A:

Q: Let us say that we have jointly distributed random variables X and Y with E(X) = 3, E(Y) = 5, Var…

A:

Q: Suppose an insect lays a very large number of eggs Y, where Y ~ Po(lambda), and suppose that each…

A: Introduction: The random variable Y denotes the number of eggs laid by a randomly chosen insect. It…

Q: (b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If…

A:

Q: O Let X be a Poisson random variable with parameter 0, then E (X²) = 1 .

A:

Q: Two random variables X and Y have the joint characteristic function Pxr (@,, a, ) = exp(-20f -8a})…

A:

Q: If X is a uniform random variable over the interval (8, 12), find E[X]

A:

Q: Suppose that the random variables X,Y and Z have the following joint probability listribution. * y z…

A: given that

Q: Let X1, X2,..., Xn be independent exponential random variables with mean if. For example, E(X1)=0,…

A:

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: f X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find…

A: Given:    X1, X2 are two independent exponential random variables with respective parameters λ1 and…

Q: Suppose X1, X2, X3 and X4 are independent random variables, which have the same Bernoulli…

A: Given that  X1, X2, X3, X4 ~ Bernoulli ( p = 1/3 ) X1, X2, X3, X4 are independent  Compute Cov(X1 +…

Q: Suppose X, Y are two discrete random variables with probability function given by: Y\X -1 1 1/8 1/8…

A:

Q: Let X be Poisson random variable with the mean λ. Find the value of λ that satisfies P(X = 0|X ≤ 2)…

A: Let X be a random variable which follows Poisson distribution with a population mean λ. X~P(λ) The…

Q: If the random variable X has a Poisson distribution where the lambda equals 7, Then the different…

A:

Q: Let Z be a discrete random variable withE(Z)=0. Does it necessarily follow that E(Z3)=0? If yes,…

A: Solution

Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: Find the distribution of Z X+Y, if X and Y are jointly continuous random variables F given by

A: Given information: The joint probability density function of the random variables X and Y is given.

Q: Given that a random variable X have a Poisson distribution with 2; Find E[cos(nX)] if E(X) = In 2

A: Given information: X = a Poisson random variable The expected value of X is: EX=ln 2=λ It is…

Q: If X is a discrete random variable with the distribution function p(x) = 3-*; x = 1,2,3 ... Prove…

A: Given that the distribution function of the discrete random variable X as px=3-x  ; x=1, 2, 3 ...…

Q: Suppose X1, X2,..., X10 are independent random variables, Find P(X1+ X2 +...+ X10 < 25), assuming…

A: It is given that X is a random variable. Therefore, Bernoulli distribution is,

Q: 2. Prove that if X is a discrete random variable, a and b are constants, and Y = aX + b, then My (t)…

A:

Q: 5. Suppose that X is a Poisson random variable with = 0.02 and t = 50. Find a. P(X > 2), b. P(1 < X…

A: Given data: Suppose that X is a Poisson random variable with (λ) = 0.02 and t = 50. To Find a. P(X ≥…

Q: (a) Show that the random variable (2/0) E X, has a x2-distribution with 2n degrees of freedom.

A: Solution

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and…

A:

Q: If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y…

A: X1,X2,X3 are same from a Bernoulli distribution. Y=X1+2X2+X3 Let X1,X2,X3 are from Bernoullip.

Q: 1. Given that x is a continuous random variable that is uniformly distributed in a range from 8 to…

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

Q: X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are…

A:

Q: Let X and Y denote two independent Poisson random variables with and .

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: X is an poisson random variable with parameter λ = 4 Calculate P {X ≤ 3}

A: It is given that X is the random variable and the mean given by λ is equal to 4 The probability of X…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.