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 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: (34) Let X be a random variable with p.d.f. 1<x<» k f(x) = { find k. O.w

A: Formula used: fx=x-2k           1&lt;x&lt;∞0                   Otherwise

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: 9) The initial cost of a random investment is negotiable. The lifetime is 5 years. The MARR is 10% a…

A: According to the above statement

Q: If X be a continuous random variable with be -bx if x >0 f(x)= otherwise then the moment generating…

A: The random variables can be categorized into 2, continuous random variable and discrete random…

Q: Suppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1,x2) = c(x1 +…

A:

Q: ). If X is a continuous random variable whose pdf is f(x): (a) 0 (b) 1 (c) 1/4 (d) 4 (e) None of the…

A: 0 \)" data-mce-style="cursor: default;"&gt;f(x)=c(1+x)4;x&gt;0

Q: Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi.…

A: Understanding the Pressure Relationship in TiresKnowing the air pressure in one tire of a vehicle…

Q: Suppose the random variable y is a function of several independent random variables, say…

A: Given that the random variable y is a function of several independent random variables, say…

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

Q: 2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution…

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 random variable with pdf given by fX(x) = 1/[π(1 + x2)] for all real number x. Prove that…

A: Solution

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: Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let…

A: X~Geometric distribution with parameter θWe have to finda.. Likelihood functionb.. Show that log…

Q: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street…

A: The random variable   represents the waiting time for the pedestrian signal. The PDF of random…

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

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

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

A:

Q: Q1 Let X be a non-negative discrete random variable. Prove that the expected value of X satisfies…

A:

Q: Let X be a random variable with p.d.f. 2e-2x f(x)=< 0<x<0 , find E(e2") O.w

A: Let  X be a random variable with the pdf  fx=2e-2x                 0&lt;x&lt;∞0…

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

A: Solution

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: 4. Probability maximization: We have independent random variables X and Y with distribution X ~…

A: This question seeks to calculate the probability maximization estimator (ϕ^) for two independent…

Q: Suppose X is a random variable and h is a non-increasing function, i.e., h(r) ≤h(2) if a1 > 2.…

A: Given X is a random variable and h is a non-increasing function.Non-increasing function:A function h…

Q: Let X,, X2, .. .be independent Cauchy random variables, each with PDF d f(x)= T(d² +x²)' Show that…

A:

Q: (16) The moment-generating function of the geometric random variable X with parameter p is M(t) =…

A: The moment-generating function of random variable X is given as, M(t)=p1-1-pet It is known that…

Q: Suppose that W is a random variable with E(W4)&lt; ∞. Show thatE(W2) &lt; ∞.

A: Given: Jensen’s inequality says that if g(.) is a convex function:

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.