Let X be a random variable with a variance of 2. Find the variance of 5X+5. Answer: Var(5X+ 5)=

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: p(x) Compute E(X), E(X²), and V(X). x ft3 (X) = x²) = (X) = If the price of a freezer having…

A: Since the question has multiple sub parts we will solve the first three sub parts. Please resend the…

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

Q: Q3/A/ Let X be a r.v with p.d.f f(x) =e-xl - 00 <x < oo, then the value of variance of X is -

A: Given :Let X be a r.v  with p.d.f f(x)=12e-|x|Formula : ∫-∞∞f(x)dx

Q: If X1, X2, .., Xn are mutually independent normal random variables, with their means all equal to 3…

A: From the given information, E(Xi)=3V(Xi)=10

Q: For every a, 0 > 0. i) Derive the expected value of X. i) Derive the variance of X.

A:

Q: (8) Find the variance of X when X is distributed as N(0, 1). The correct answer is -1 1 -2 N/A…

A: Given that that X~N(0,1).

Q: When you are conducting the t test, the population does NOT need to be approximately normally…

A: one of the assumption for conducting t-test is that when you are conducting t-test the population…

Q: A random variable has a CDF given by: '0, x 1, (a) Find the mean of X (b) Find the variance of X

A:

Q: If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are…

A: Solution

Q: Q3/A/ Let X be a r.v with p.d.f f(x) =;e-lkl - 00 <x < 0, then the value of variance of X is

A: 3. Given information: It was stated that X is a random variable and the probability density function…

Q: 2n- 50 and p= 0.45

A: Given, Let, n =number of trials p =the probability of success q=1-p

Q: = Let X₁, ..., X, be a random sample from EXP(0), and define 0₁ Đ, = nX/(n + 1). 2 (a) Find the…

A:

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. .…

A: X follows a  normal distribution with , µ= -1 , σ= 1. Y follows a  normal distribution with , µ= 1 ,…

Q: Q2. If the lifetime X of a hearing aid battery has Weibull distribution with a = 0.1,ß = 0.5. Find…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If X and Y are independent random variables with variances σ2 X = 5 and σ2 Y = 3, find the variance…

A: Given:VX=5 and VY=3

Q: (E}=1 x?); i3D1 8075 so what is the variance of these population (N=8).

A: sum of x = 243 therefore mean  = 2438 = 30.375 sum of squares of x = 8075

Q: Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression…

A:

Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: Let X be a random variable with a mean of 50 and a variance of 64. Find: i. P(x< 52) ii. P(35 < X <…

A:

Q: 20. The lines of regression of y on x and x on y are, respectively, y= x+ 5 and 16x -9y 94. Find the…

A:

Q: 5.lf two samples are selected from the same population, under what circumstances will the two…

A: We uses t-test to test the hypothesis about an unknown population mean.

Q: Y is a random variable and "a" and "b" two real constants. Without resorting to the properties of…

A: Given that, Y is a random variable and "a" and "b" two real constants. Without resorting to the…

Q: Use this covariance matrix to find the estimated variance of the estimated mean of y when z = 8.…

A:

Q: Let the random variables Y, Y2, ... , Ys be normally distributed with mean 10 and variance 4. Find a…

A: Given that Yi, i = 12,3,4,5 follows N(mean = 10, variance = 4)

Q: Find the variance of the random variable Z = 1−Y

A: Given that, Y denotes the proportion  of impurities in a batch and density function of Y : f(y) =…

Q: Let X1,…,Xn be i.i.d. Exp(λ) random variables, where λ is unknown.What is the variance and quadratic…

A: The pdf of min (xi) is as follows: Thus, min (xi) follows exponential distribution with parameter…

Q: If the variances for independent random variables X and Y is Var(X)=0.94 and Var(Y)=4.22 then Var…

A: The given variances for independent random variables X and Y are Var(X)= 0.94 Var(Y) = 4.22 We have…

Q: A discrete random variable U can take the values (-4,-1, 2, 3, 4) with the same probability of 1/5.…

A: Given: Let the discrete random variables be U and U = {-4, -1, 2, 3, 4}

Q: Then the value of the variance of X+Y is:

A: Variance of X + Y can be calculated as V(X + Y) = V(X) + V(Y) + 2Cov(X, Y)

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x =0 (ii) 1Sx<4 eor…

A: GivenThe variance of a poisson variate is 3in poisson distribution the parameter of mean and…

Q: Consider a random sample from the distribution of Binomial, Poisson, Exponential, Gamma, and normal.…

A: Binomial: Let Xi~Bn,p, the the p.m.f of Xi is given by, px=nCxpxqn-x,x=0,1,2,...,n Then, EXi=np and…

Q: Find the variance of X + 3Y + Z + 6 in terms of the variances and covariances of X, Y, and Z.

A: Given:  X + 3Y + Z + 6

Q: If the variances for independent random variables X and Y is Var(X)=0.7 and Var(Y)=7.45 then Var…

A:

Q: If X Gamma(4,6) the the variance of X is 4 24 144

A:

Q: 4) Find the variance V(X).

A:

Q: The service times for customers coming through a checkout counter in a retail store are independent…

A: Given that μ=1.5,σ2=1.0, n=100 P1.5-y0≤Y¯≤1.5+y0=0.95

Q: 3x (1+х) Q2. If f(x) = ; 0<x <2 denotes the pdf of a continuous random variable, find mean 14 and…

A: Mean = E(X) = ∫xf(x)dx Variance = E(X2) - E(X)2 Where ,   E(X2) = ∫x2f(x) dx

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: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…

A: The given pdf is shown below:

Q: Let X be a random variable with expected value E(X) = 1 and variance Var(X) = 4. Find E(3X +2) and…

A: From the provided information, E (X) = 1 and Var (X) = 4

Q: The variance of a random variable (X+ a) is equal to the variance of the random variable X itself

A:

Q: Find the expected value and variance of F

A: Given :  (i) The expected value and variance of  (ii)

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

A:

Q: 5A+2B. The variance of T is 6

A: The random variables A and B have variances 0.2 and 0.5 respectively. Let T= 5A+2B.

Q: Q1. If Var(X)=3, what is Var(2X + 1)? Q2. Compute the variance for a uniform random variable with a…

A:

Q: Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater…

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: The conditional expectation of Y given X-x is x 00 The conditional variance of Y given X-x is ²

A:

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.