Q. 1 A machine produces 1% defective components is used for a production run of 40 components. (i) Calculate the probability that two defective items are produced using (a) the binomial distribution and (b) its Poisson approximation. (ii) Let random variable X is defective components then find E () and Var ().

Q: Let X be a discrete random variable with PMF Px(X) = { (0.5, x=2) (0.3, x=5) (0.2, x=6) (0,…

A: Let X be a discrete random variable with PMF Px(X) , and CDF F(X), the CDF is defined as F(X) = P(X…

Q: Let X₁, X₂, ..., Xn be a random sample from a Beta distribution with the pdf f(x; a) = axa-1 for 0 <…

A:

Q: 1. A random variable X has following probability distribution function: f(x) = c(x − 1)2, x =…

A: ### Part (a) Finding  cThe given probability distribution function is:f(x)=c(x−1)2−x,x=2,3,...Since…

Q: 2)Consider a random variable X with MGF M(t) = e³t+4t² Find the mean and variance of X.

A: Question 2)The moment generating function (MGF) of a random variable  is, The objective is to…

Q: (a) A lower bound for P(6<Y <24) (b) the value of k such that P(|Y-15| ≥k) ≤ 0.09.

A:

Q: Given that the random viriable X has mean µ = 90 and SD e= 15, find the mean and SD of each of the…

A:

Q: Let Y₁, Y₂, and Y be independent, identically distributed random variables from a population with…

A: Dear student, If you find this solution helpful please upvote it. The solution is given below :

Q: If X is a random variable for which E (X) 10 and Var (X) = 25, for what positive value of 'a' and b'…

A:

Q: 2. Show how the Poisson distribution -m m e (x= 0, 1, 2,...) %3D х! can be regarded as the limiting…

A:

Q: Random variables X and Y have the means and standard deviations as given in the table to the right…

A:

Q: Let X denote a random variable that has a Poisson distribution with mean 1= 2. Find (a) P(X = 4) %3D…

A: Here X~ Poisson with parameter 2. We need to find the required probabilities.

Q: Let X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random…

A:

Q: A random variable X is uniform from 4 to 8. A Gaussian random variable Y has mean of 10. Approximate…

A: Given: A random variable X is uniform from 4 to 8. A Gaussian random variable Y has a mean of 10.…

Q: A noisy resistor presents a voltage X distributed as a Gaussian random variable with zero mean and…

A: X : voltage of a noisy resistor    Therefore,  X ~ N(mean : μ = 0, standard deviation : σ = 2 =…

Q: Suppose X and Y are independent. X has a mean of 1 and variance of 1, Y has a mean of 0, and…

A: According to the Bartleby guidelines expert solve only one question and maximum three subpart of the…

Q: Find the standard deviation of a discrete random variable X which satisfies P(X=1)=0.1,P(X=-1)=0.6,…

A: Given: A discrete random variable X satisfies the following:     P(X=1)=0.1P(X=-1)=0.6    P(X=2)=0.3

Q: Let X be the Random Variable: x | P(X = x) 0.5 0 1 0.2 2 0.3 Let X1, X2 be the identically…

A:

Q: A random variable X has a distribution with probability function f(x) = k for x = 1, 2, ... (a) Find…

A:

Q: If E denotes the expectation (random variable X is denoted the variance of a as (E(X))^2 - E(X False…

A: Given,E denotes the expectation .

Q: Determine the mean and the ontinuous) random variables with the following moment-generatir M(t) = (1…

A: The moment generating function is M(t)=(1-4t)-2

Q: The random variables , $1, 2,... are independent and identically distributed with distribution P( =…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: (i) Show that c = 2 (ii) Calculate the mean and variance of X. (iii) Find the CDF of the random…

A: As per policy I have calculated first 3 subparts plz REPOST for remaining parts with note I need…

Q: Suppose the probability function for x is such that p(x=1)=0.3, p(x=2)=0.4 and p(x=3)=0.3. What is…

A:

Q: Calculate the variance of a random variable X whose characteristic function is (1+ e3it)² f(t) = 4

A: We have given that the characteristics function of random variable X and we have to calculate the…

Q: 1. A discrete random variable X follows the Uniform distribution if X takes values x = 1, 2, .., N,…

A: It is an important part of statistics. It is widely used.

Q: Let X1,.., Xn, be a random sample from the following probability distribution x+1 fX(x)=0De-*/", x >…

A: Solution:  a)  fX(x)  = x+1θ(θ+1) e-xθ             : x &gt;0 and θ&gt; 0 Joint pdf is given by,…

Q: Let x1, x2,..., n represent a random sample from a distribution with mean E(x) and variance Var(x).…

A:

Q: If a random variable X has the moment generating function M,(t) = %3D 2-t' determine the variance of…

A: Given,Mx(t)=22-t

Q: Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the…

A: Given data: Mean = 6 Variance = 4 Thus, Std. Dev = sqrt(variance) = sqrt(4) = 2

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.