25) Let Y be a discrete random variable, with probability function py given by 1/2y 1/2|y| y = 2, 4, 8, 16, ... у%3D— 2, —4, -8, —16, ... otherwise. PY (y) = py (y) Compute expectation of random variable Y.

Q: Let X~N(2,1), Y~N(-1,2). X and Y are independent. Find the probability distribution for Z=X - 2Y.

A: The probability density function of normal variable is given by, f(x)=1σ2πe-12x-μσ2 Given: X~N(2,1)…

Q: The discrete random variable X has the probability distribution 2 4 P(X=x) k 2k 3k 4k 3.

A:

Q: If 'X' is a continuous random variable, then the expected value is given by O a. SXP(X) O b. No…

A: The symbol used to denote the expected value of a particular random variable is E(X). It is defined…

Q: Q1) A discrete random variable x has the probability distribution p(X = k) for occurrence of x as…

A: We have given a discrete random variable.x       0  1    2   3  p(x)   k  2k 3k 4kWe have to…

Q: (a) f(x) = c(x² + 6), for x = 0, 1, 2, 3 5 3 - (:) ( 2² X (b) f(x) = c 3-x for x = 0, 1, 2

A: It is given that a probability distribution of the discrete random variable X.

Q: Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X).

A:

Q: The probability generating function for a random variable X is given by: gx(2) ==z? +10+z20+25 (2)X6…

A: From a given probability generating function of X, we need to find required conditional probability.

Q: (1) Let X be a random variable with a function [A(3x² +6) -1,0,1,2 . then (0) k = (6) k = (e) * (d)…

A:

Q: b) Let Y, and Y, be discrete random variables with a joint probability distribution as shown in the…

A: Given: The joint probability distribution of the random variable Y1 and Y2 is provided as:…

Q: ) Let X and Y be two discrete random variables. Their joint probability mass function is as follow…

A:

Q: A grade in a probability course depends on exam scores X1 and X2. The professor, a fan of…

A: As per guidelines of Bartleby,we are giving here solution of first 3 parts only.

Q: The cdf of a random variable Y is |1– exp(-0.4y), y 20 F,(y) otherwise Valuate P{2.5 <Y < 6.2}.

A:

Q: Let X and Y be independent random variables such that E(X)=2, E(Y)=2, var(X)=2, and var(Y)=2…

A: We know that, If X and Y are independent random variables.  Var(X+Y)= Var(X)+ Var(Y)

Q: Let X1 ~ N (0, 1), X2 ~ N(0,1), and X3 ~ x(n) be mutally independent random variables. Find the…

A: Given information X1, X2 follows normal and X3 follows the chi-square distribution General condition…

Q: Let X be a random variable taking only the values 0, 1, 2, 3, 4 with probabilities given by P(X = 0)…

A: Discrete probabilty  The conditions of the probability is 1) p(x) ≥ 0 2) Σp(x)=1

Q: Find k if the joint probability distribution of X, Y, andZ is given by f(x, y, z) = kxyzfor x = 1,…

A: The joint probability density function is given as f(x,y,z)=kxyz For x=1,2 ;y=1,2,3 ,z=1,2. Compute…

Q: Let X be a random variable with probabilities as shown in Table 3.7. Table 3.7 Values of X and P(x)…

A:

Q: 1.) The amount of time an air-conditioning technician to repair a unit is in between 1.9 and 5 hours…

A: Given data: X ~ U ( 1.9 , 5 ) To find: Find the probability that a randomly selected A/C unit repair…

Q: The probability generating function for a random variable X is given by: z2우 = (2)XG z10 +z20+. P(X…

A: Given a probability generating function of X, we need to find P( X &lt; 5 | X &lt; 13)

Q: Determine E(x) and E(y)

A: The given probabilities are…

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.