If a random variable X has mean 3 and variance 4, then E(X² + 3X + 2) is

Q: Suppose that X is a random variable which only takes on non-negative values, with mean 5 and…

A:

Q: If X is normal random variable with mean 3 and variance 5, then find the probability P(2 < X <6).

A:

Q: Q7- If the random variable X is normal with mean 4 and standard deviation 2, then what is P(X² – 8X…

A: Given: X~ N (μ=4 ,  σ = 2) mean= μ = 4 standard deviation = σ = 2 Calculation: then find  P(X2-8X…

Q: Since P {x=-1} = P {x=1} = 1/2 , calculate the expected value and variance of the X random variable.…

A: Solution: From the given information,

Q: Given two independent random variables X and Y with means and standard deviations given by μ X = 5 ,…

A: It is given that the variables  X and Y are independent.

Q: 5. Show that for a discrete uniform random variable X, if each of the values in the range of X is…

A:

Q: 4.62 If X and Y are independent random variables with variances o of the random variable Z = -2X +…

A: Given that Var(X) = 5 And Var(Y) = 3

Q: 4. The expected value of a random variable X is 10 and its variance is 16. If the random variable X…

A:

Q: 4.62 If X and Y are independent random variables with variances o = of the random variable Z = -2X +…

A: 4.62: Given that X and Y are independent random variables with variances σX2=5 and σy2=3. And σXY=0…

Q: Suppose that X and Y are independent random variables having the joint probability distribution:…

A: Joint Probability Distribution: Let there are two random variables X and Y. Then the joint…

Q: Suppose that the cumulative distribution function of the random variable X: x —1.5)

A:

Q: The covariance of two random variables is always a number between -1 and 1 True False

A: In this case, we need to find the correct option.

Q: Suppose X and Y are independent random variables with expected values E[X] = 0, E[Y] = 0, and Var(X)…

A: We have given that  X and Y are independent random variables with expected values E[X] = 0, E[Y] =…

Q: If X is a normal random variable with parameters µ = 3 and o² = 9, find P(2 0). с. P(|X – 3| > 6).

A:

Q: If X and Y are independent random variables with means μX = 9.5 and μY = 6.8, and standard…

A: Solution: a. From the given information, µX=9.5, µY=6.8, σX=0.4 and σY=0.1. The mean of 3X is

Q: A normally distributed random variable X with variance = 400 and P(X > 120) = 0.7632. Then the mean…

A: Let X be the normally distributed random variable with variance σ2=400 X~N(μ, σ2=400)

Q: Since P {X = -6} = 1/6, P {X = 3} = 1/3, P {X = 4} = 1/2  , Calculate the expected value and…

A: Expected value:E(X)=∑xipi=-616+313+412=2

Q: 2. Suppose the cumulative distribution function of the random variable X is x < -2, - 2 < x < 2, 2<…

A:

Q: IF the variance of the discrete random variable X =36 * (2 Points) and if E (X²) = 100 , then E (X)…

A: We have to find E(x)..

Q: Suppose you take a stock returns from the Excelsior Corporation and the Adirondack Corporation from…

A:

Q: If a random variable that follows exponential distribution shows that P(X2000)=0.7, Then P(30002000)…

A: Exponential probability distribution has memoryless property i.e. P(X &lt; a   | X &gt; b) = P(X…

Q: Group A is a sample of 15 people and has a Sum of Squares of 1200 Group B is a sample of 15 people…

A: From the provided information,

Q: If the mean of a discrete random variable is 3 and its variance is 2, find u,. O 1 O 2 9. O 4

A:

Q: Suppose you have a chi-square random variable, Y, with 10 degrees of freedom. What is the smallest…

A: Given: Y~χ102   PY&gt;k&lt;0.05  ................(1)

Q: A discrete random variable X has variance 3. Which of the following is the variance of 3X - 2? 25 3…

A:

Q: Let X be a random variable with mean µ and variance σ^2. Let Y = aX2 + bX + c. Find the expected…

A: From the given information, it can be written as follows:

Q: Suppose X is an exponential random variable, and E(X) = 2. Find the probability that X will be…

A: Given, μ=2  σ2=22 σ=2   Probability density function of x is, p(X=x)=12e-x2…

Q: Let X be a binomial random variable with n=7 and p=0.1, then The variance of X is 0.63 P(X>1)=…

A: Given: n=7 and p=0.1 Then, the variance isVariance=np1-p=70.11-0.1=70.10.9=0.63

Q: Let X be a random variable with an expected value of 0, and let X² have an expected value of 9. Find…

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: Find the mean and the variance of the discrete random variable X, whose probability distribution is…

A:

Q: A normally distributed random variable X with variance o = 400 and P(X > 250) = 0.7425. Then the…

A:

Q: If the random variable X is binomially distributed with p-0.75 and o-0.7125, then P(X=1) is

A: The provided information are: Meanμ=0.75Varianceσ2=0.7125

Q: In analysis of variance problem if SST = 150 and SSTR = 100, then SSE is

A: It is known that, SSE = SST-SSTR.

Q: The mumber students who enter a Library in an hour is a poisson random variable. and suppose that…

A:

Q: Suppose X is a uniform random variable on the interval (1, 3), and E(X) = 2. Find the probability…

A: X follows uniform (1, 3). That is, fx=13-1=12VX=b-a212SDX=b-a12=3-112=212=13

Q: Given a random variable X with mean ux and variance ož, find the mean and variance of the random…

A: Given, Mean Of Random Variable X : EX=μX Variance Of Random Variable X : VarX=σX2 New Random…

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: Let X is a Gaussian random variable with zero mean an variance o · Y = X. Find mean of Random…

A:

Q: 1. Let X₁ and X2 be two independent random variables with respective means 3 and 7 and variances 9…

A: Given that, Let The mean of Y is,

Q: Assume that you have a random variable X which is binomially distributed, and someone told you that…

A: Assume that you have a random variable X which is binomially distributed, andsomeone told you that…

Q: Suppose X is a random variable distributed with mean u and standard deviation ơ > O. If the random…

A:

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

A:

Q: 6- The Variance of X, is a) o? b) d)

A: we want to find value of the variance of xbar n is ...

Q: Let X be a random variable with the following probability |-6 3 9 distribution: 1 f(x) 4 1 1 2 4…

A: Given X is random variable with the probability distribution: x -6 3 9 f(x) 14 12 14 and…

Q: If Xis a random variable having a binomial distributionwith n = 20 and p = 0.4, and Y is a…

A: The random variable X has a binomial distribution with n=20 and p=0.4. Here Y=2X+3.

Q: Let X1 ~ N(41, 0?) and X2 ~ N(u2, 03). Find the expected value and variance of Y = X1 + X2.

A: Solution: 39. From the given information,

Q: In an analysis of variance problem if SST = 120 and SSTR = 90, then SSE is

A: It is given that SST =120 and SSTR = 90.

Q: If x is a binomial random variable with n = 10 and p = 0.8, the standard deviation of x is…

A:

Q: Suppose that the cumulative distribution function of the random variable X: x -1.5)

A:

Q: b) Suppose that 10% of the values of a normally distributed random variable X are below 50, and 5%…

A: Assume, X be the random variable. It is mentioned that X follows normal distribution with mean μ and…