3- If f(x) = k is the probability density function for a random variable that can take on the values x = 0, 1, 2, 3 and 4, then the cumulative function is 2x 32/2x+1 (a) 3² (²24¹) 2x+1 31 x+1 (c) ¹ (²+¹) 2x+1 2x+1 -1 (b) (²+¹) 2x+1 (d) (²) x+1, a b

Q: The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a…

A: Given, The probability mass function is: 0 1 2 3 4 5 1/12 1/12 3/12 4/12…

Q: If the random variable X and Y have the joint probability distribution f(x, y) = x+y, 0<x< 1,0 <y<1…

A:

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: Given that 40% of fruit flies of fruit flies posses a certain gene. So, probability that a fruit fly…

Q: If X is a random variable with probability density function 32 f (x) = for x = 0, 1, 2, 3, 4 and 5,…

A: Formula : Variance :

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: Random variable X has the following probability mass function: P(X=x) = (x+1)/12 for x = 0, 1, 2, 5.…

A:

Q: If the joint probability distribution of X1 and X2 isgiven by f(x1, x2) = x1x236for x1 = 1, 2, 3 and…

A:

Q: A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x-x²+4) =

A: Given that E(X) = 1.5, and var(X) = 0.25 The var(X) is defined as Var(X) = E(X2) - (E(X))2

Q: а. Р(Х <- 2) b. Р(-1 <х < 1)

A:

Q: The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a…

A: Given, Te probability mass function is: 0 1 2 3 4 5 1/12 1/12 3/12 4/12 2/12 1/12     To…

Q: Determine the values of c so that the following functions represent joint probability distributions…

A: (a) Given that the joint probability distribution of the random variable X and Y is   f(x,y)=cxy,…

Q: X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X +…

A: We want to find V(aX+bY)= ?

Q: Let Y be a continuous random variable with cumulative distribution function: B A C C D D E √2 In √√2…

A: We have to find 75th percentile of Y :

Q: 1+3x 1-4x (10) If a random variable assumes 4 values with probability 1+1 1+2 and the condition on x…

A: A random variable assumes 4 values with probability p1=1+3x4 , p2=1-x4 , p3=1+2x4 , p4=1-4x4

Q: 7- Let X be a random variable with probability density function x=1,2,5 f(x)=8 O.w. (a) Find the…

A: Result used  Y=ax+b  E(Y)=aE(X)+b  V(Y)=a2V(X)  Var(X)=E(X2)-(E(X))2

Q: Fact: If X is a compound random variable with X = ₁X₁, ther E(X) = E(X₁) E(N) a. when X are all…

A:

Q: P (X) = x / 10 if,  X = 1, 2, 3, 4 is a probability distribution for the random variable X. True…

A: We have to find true or false.

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: e non negative integer valued random variable X has obability generating function Gx(s) = log. ( )…

A: Given:  Non negative integer random variable x with probability generating function…

Q: B) Let X and Y be discrete random variables with joint probability function 2-y+1 9 for x = 1,2 and…

A:

Q: Let X1 and X2 be discrete random variables with joint probability distribution x1 = 1, 2; x2 = 1, 2,…

A:

Q: 2. If the random variable Xhas the probability density function ƒ(x) = ³(1 − x²), −1 < x < 1, what…

A:

Q: Let the probability function of the random variable X be f(x) = {  x/45 if x = 1, 2, 3, ⋯ ⋯ ,9…

A:

Q: Let joint Probability distribution function of random variables X and Y be (1/3 if (x, y) = (1, 1)…

A: The joint probability distribution function for X and Y is, P(x,y)=13, if(x,y)=(1,1)13, if…

Q: as an order pair, (R, B) where R and B are numbers from the red and ly. Let X be a random variable…

A:

Q: let x be a discrete random variable with probability function p(x)= cx/20 for x = 2,3,4,5,6,8,12…

A: