3. Consider the random variables Y1,..., Yn that satisfy Y; = Bx; + €i, i = 1, ...,n. where ¤1,.., In are fixed constants, and €; are i.i.d. random variables that follow N(0, o²) where o² is unknown. (a) Find the mle B of B and show that it is an unbiased estimator of 3. (b) Find the distribution of the mle of ß.

Q: 1. Let X be a Binomial random variable with n = 3 and p = 0.4: X~ Binomial(3, 0.4). a) Fill in the…

A: X be a Binomial random variable with n=3 and p=0.4X~Binomial(n=3,p=0.4)P(X=x)=nx×px×(1-p)n-x    ;…

Q: The random variable, X, representing the number of cherries in a cherry cake, has the following…

A: The random variable x denotes the number of cherries in a cherry cake.

Q: 17. It assumes an infinite number of possible values including the decimal between two counting…

A: #17 Here we have given the multiple choice question about the random variable. There 2 types of…

Q: .a. X is a discrete random variable that takes values (1, 2, 3, 4, 5). If, P(X=3)=0.5 and F(4)=0.85.…

A: a) It is given that P(X=3) =0.5 and F(4) =0.85.

Q: 3.5 Determine the value c so that each of the follow- ing functions can serve as a probability…

A: We have given that the probability distribution of discrete random variable X. In discrete…

Q: Suppose that the number of accidents occurring on a highway each day is a Poisson  random variable…

A: Givenλ=3.1 for each dayLet "x" be the no.of accidents occur in a dayx~Poisson(λ=3.1)P(X=x)=e-λ×λxx!…

Q: Q5. A) Consider a sample X,,X,*,X, of normally distributed random variables with variance o= 11.…

A: Note: As per Bartleby’s guideline for more than one questions only first is to be answered please…

Q: Suppose data X1, ..., Xn are sampled from the population, sample mean is a random variable

A: It is given that Sample : x1, x2,......,xn

Q: Find the CDF of an exponential random variable with mean 1/λ .

A: Solution

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 random variable from a Chi-Square Distribution with 13 degrees of freedom. Tatiana is…

A: We have to answer questions based on chi square distribution.

Q: A. Classify each random variable as discrete or continuous 1. X: Number of women among 10 newly…

A: Since you have posted multiple sub-parts of question , we will solve first 3 sub-parts for you. To…

Q: Let X1 , X2 ,....., X25 be a random sample drawn from a population with mean of 75 and standard…

A: Given data, μ=75σ=25n=25µx=?

Q: suppose that X is a random variable with probability distribution.P(X=k)= 0.02k,where k takes the…

A: Given: P(X=k) = 0.02k k = 8,12,10,20 Here takes the value 8,12,10,20

Q: Let (x1, x2,.., xn) be the observed values of a random sample for a Gaussian random variable X. Find…

A:

Q: Question 2. Let X be a normal random variable with u = -5 and o² = 4. a) Find P(X –3|X > -5).

A:

Q: 4. Let X₁ N(0,3²), X₂ N(4,42), and X3~ N(-1,22) be independent random variables. Find P (X₁ + X₂…

A: X1~N(0, 32 ), X2~N(4, 42 ) , and X3~N(-1, 22 ) be independent random variables.

Q: Let Y be an exponential random variable with (unknown) mean 0.

A: Mean of Y is θ

Q: If X, = 2, X, = 3, X, = 1, X, = 4, X, = 1, and X, = 8 be a random sample taken from a population…

A:

Q: Let X1, X2, X3… X20 be a random sample from a distribution with mean 8 and variance 5. Find the mean…

A:

Q: Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and…

A: a) T=3X+12Y-2Z To Find: E(T) E(T)=3E(X)+12E(Y)-2E(Z)=3×7+12×(-2)-2×5=13 Answer: 13

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.