Suppose X is a discrete random variable with pmf defined as p(x) = log10 fo x = {1,2,3,...9} Prove that p(x) is a legitimate pmf.

Q: Let X1, X2,...,X, be a set of independent random variables each following the distribution with pdf…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let X be a discrete random variable with the following moment generating function: (1/2) e' M(t) - 1…

A: Solution: From the given information, the moment generating function is

Q: Suppose that Y ~ Normal(0, 1) and define new random variable X by X=Y². Compute ELYI

A: Given that Y~Normal0,1 Here, E(Y)=0V(Y)=1⇒E(Y2)-EY2=1⇒E(Y2)-0=1⇒E(Y2)=1

Q: Find fQ|X (q|x) for x ∈ {0, 1} and all q.

A: It is a fact of statistics. It is widely used.

Q: 3. Let the random variable X have the pmf f(x) = = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² for x =…

A: The provided information is as follows:The probability mass function of  is .

Q: Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . .…

A: Probability Mass Function :- If X is a One-dimensional discrete random variable taking at most a…

Q: Suppose that Y₁ = 0.5, Y₂ = 0.6, Y3 = 0.2, Y4 = 0.7 and Y5 = 0.6, represents a random sample. Each…

A: Solution

Q: Let Ybe an exponentially distributed random variable with mean ß. Define a random variable X in the…

A: Y is an exponential random variable with mean β . Therefore, the PDF of Y is:Result:∫eaxdx=eaxa

Q: Give the following answers to three decimal places, where appropriate. (c) Find the expected value…

A:

Q: 17. Let X1, X2, and X3 be independent, U (0, 1)-distributed random variables. Compute P(X(3) > 1/2|…

A:

Q: ). Let M = ln(5*X) be a derived random variable. What is E[M]?

A:

Q: 4. If the random variable X has an show that for a > 0, b>0, exponential distrib f(x) = x/4, for x ≥…

A: For the random variable X~Exponential1λ, it is given that: fx=1λe-xλ, for x≥0

Q: Let X₁, Xn be a random sample from the beta distribution with a = B = 0 and = = {0: 0= 1,2}. Show…

A:

Q: random process of x(t) is defined by x(t)=Acos(at) + Bsin(at), where A and B are two andom variables…

A:

Q: Let X be a positive random variable; i.e P(X ≤ 0) = 0. Which one is correct? (1) E (+) (²) (11)…

A: Given:X is a positive random variable, meaning .We need to determine which of the statements is…

Q: Let X be a Uniform(-9,9) random variable. (a) The moment generating function of X is Mx(t) = A(eBt –…

A: X∼U(−9,9)  and is an independently drawn from U(−9,9)Objective:Find moment generating function…

Q: Let X be a continuous random variable with pdf f(x) = x² for -1 < x < c. Find the value of c.

A: From the given information, the pdf of the random variable X is,

Q: 3. Consider two random variables X₁ and X₂ whose joint pdf is given by 11/2 for x₁ > 0, x2 > 0, x1 +…

A: We are given joint PDF of X1 and X2 as,f(x1,x2)=12;for x1&gt;0 and x2&gt;0, x1+x2&lt;0…

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.