Let X1, X2,X3,X4 be independent random variables each with E(X) = 0 and Var(X) = 1 for i= 1,2,3,4. Let Y = X1 + X2 +X3 + X4, then Var(Y) = Select one: a. b. 4 С. 1 16 d. 16 1/4

Q: ii) Let X be a random variable taking three values: P(X= a₁) = P₁, P(X=a₂) = P2, P(X=a3) = P3, where…

A: Given Information: Let X be a random variable taking three values: PX=a1=p1, PX=a2=p2, PX=a3=p3,…

Q: Assume both follow a Normal distribution. What can be concluded at the a = .01 level of…

A: Given: n1 = 10 n2 = 10 α = 0.01 Formula Used: Test-statistic t = X1-X2sp1n1+1n2 sp =…

Q: We have the following information about the random variables X and Y: 4 8 11 4 225 , Cou (X, Υ) -…

A: The formula to obtain the variance between the two random variables when they are not independent…

Q: 1. The height of male giraffes follows a normal distribution with μ = 18 feet and o = 0.9 feet². (a)…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a…

Q: If X and Y are independent random variables with V(X)=9, and V(Y)=4 Find the Variance of the random…

A: If Z= 2X+3Y-4 Then  V(z)= 22V(X)+32V(Y)

Q: 20 families live in a neighborhood: 4 have 1 child, 8 have 2 children, 5 have 3 children, and 3 have…

A: According to the given information, X Frequency P(X) 1 4 0.2 2 8 0.4 3 5 0.25 4 3 0.15…

Q: There are three random variables X, Y and Z,for which we know the following information E(X)= 6,…

A: Given,V(X)=18  ,  V(Y)=22   ,   V(Z)=4Cov(X,Y)=-12   ,  Cov(X,Z)=5Cov(Y,Z)=8

Q: 2. Let X and Y be random variables such that V(X) = V(Y). Show that Cov(X + Y, X - Y) = 0.

A: we have given that  V(X)=V(Y) and C(X,Y)=C(Y,X)   ,C(X,X)=V(X) ,  C(Y,Y)=V(Y)

Q: Let x = (x1, x2 ..., xi, ..., xn) be a data set with a sample mean x̄ and a sample variance Sx2.…

A: Given  x=x1,x2,…,xny=y1,y2,…,ynx=x1+x2+....+xnny=y1+y2+....+ynn Given  z=x-y…

Q: A9. Let X and Y be independent standard normally distributed N(0, 1) random variables. What is…

A: Given that  X and Y are independent standard normal distribution N(0 , 1).

Q: Suppose that X andY are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y?) = 30 and…

A: Given that ; E(x) = 2   ;    E(x2 ) = 8  ; E(y) = 5  ;    E(y2 ) = 30 By using these information we…

Q: Let X and Y be independent random variables. Which statements are true? Select one or more:   a.…

A: We know that,  If X and Y are two independent random variables,  Then,  These Statments are true :…

Q: Let X₁, X₂ be independent random variables with mean and variance o, and a is a constant. We also…

A: Given that X1,X2 be independent random variables with mean μ adn variance σ2. So, E(X1)=μ=E(X2) and…

Q: Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n…

A: Solution

Q: 6. Suppose X is a random variable with E(X) = 4 and Var(X) = 9. Let Y = 4X + 5. Compute E(Y) and…

A: In question, Given E(X) = 4 and Var(X)=9 Y=4X+5 Then we'll find the value of E(Y). The solution is…

Q: The variance function will be OV(Y|X) = 0² O Bo + B₁ X + 0² O None of the other answers O V(Y|X) =…

A: It is given as the simple linear regression model Y = β0 + β1X + e,   e ~iid N( 0, σ2 ),  i = 1, 2,…

Q: 2) Given, f(x)= (2x+1)/ 25, x= 0, 1, 2, 3, 4 Determine the mean and variance of the random variable.

A:

Q: Let X and Y be random variables with Var (X₂) o and Var(Y₂) o for all ie {1,...,n}. Assume that each…

A: (a) The covariance between Xi and Yi is given by: Cov(Xi, Yi) = E[(Xi - E[Xi])(Yi - E[Yi])] Since…

Q: The random variables X and Y are independent with E(X) = 10, E(Y) = 3, Var(X)= 7 and Var(Y) = 5,…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!