Let Z be a discrete random variable with E(Z) =0. Does it necessarily follow that EC 7³ ) = 0 ? If yes give a proof; if nogice a Counter example.

Q: If X, Y and Z are three random variables, then cov (X +Y,Z) =cov(X,Z)+cov(Y,Z)

A: Solution

Q: 4 2 The probabilities of X, Y and Z becoming managers are and respectively. The 9. 3 probability…

A:

Q: A random variable has CDF given by JA i = 0,1,2 1 i = 3 if A = 0.38, then what is po? F; =

A: The CDF of the random variable is given as follows:

Q: The CDF of two random variables X and Y is given by: FxY = a [A + tan + tan For this to be a valid…

A: X,Y are jointly distributed random variable and FX,Y is the joint CDF.  FX,Y will be a valid CDF if…

Q: b) The events M and Y are independent such that P(M) = a,P(Y) = 0.3, and P(M n Y) = 0.15. i) Find…

A: b)GivenP(M)=aP(Y)=0.3P(M∩Y)=0.15

Q: 11 and ơ-2. Find each of the Suppose x is a normally distributed random variable with following a)…

A: This question has multiple parts. In such cases, we are required to answer the first 3. These 3 will…

Q: In a city, 6% of the population smokes cigars, 14% of the population smokes cigarettes, and 84% of…

A: We will find out the required values.

Q: 7) Let X a random variable with pmf P(X = x|N) =*= 1,2,..N, and let Y = 2X +1, where a, be R then EY…

A: The pmf of X is PX=x|N=1N The expectation of X is given by…

Q: 5. A random variable X is uniformly distributed over the interval (48,96). Find the following…

A: Note : As per the Bartleby guildlines we have to solve first three subparts and rest can be…

Q: If X1, X2, ,X, be n independent random exponential variables, each having a parameter ), .......S…

A: Since sum of exponential distribution is gamma distribution

Q: a) Let X, Y and Z be random variables. Show Cov(X + Y,Z) = Cov(X,Z) * Cov(Y,Z). %3D

A: Note: Hey there! Thank you for the question. Each of the questions (a), (b), (c), (d), and (e) is a…

Q: Let ( S,20 be a simple random walk starting from 0. Let P(S = 1) = p. If the probability that the…

A: Given that Snn≥0 be a simple random walk starting from 0.

Q: Suppose that c is a real number and U is a discrete random variable with E(U) = 0. Which of the…

A: Given that U is a discrete random variable with E(U)=0Let us assume that U=-1 , 1U=-1 occurs with…

Q: Suppose the discrete random variable of interest, x, is the number of rolls that result in a…

A: 8) From the given information, a dice is rolled three times. The given events are:C:{composite…

Q: Question 4. a) Let X be a random variable and let EX] = µ < o, V[X] = o². Find a random variable Y…

A: Hello thank you for the question, As you have mentioned question number 'a', answering only the…

Q: 5. Let the non-homogeneous Poisson process has the following intensity a(t) = -t² + 2t+8, 0≤t≤4 a.…

A: In this problem, we are given the intensity function of a non-homogeneous…

Q: b) The two dimensional random variables (X.Y) has a joint density function 1+x+y+cry c+3 (x, y) =-…

A: Answer:-

Q: P(X< 1 |Y = 2)

A: Given, To find the value of

Q: 1. For a nonnegative integer-valued random variable Y, show that EiP(Y >i) =LE(Y*)– E(Y)].

A: The expectation formula is as follows:

Q: If the random variable (x) has an exponential distribution with (mean=5) then the probability that…

A: Given information-

Q: Bn be independent events. Show n P(ŰB₁) = 1 - (1 - P(B;)).

A:

Q: If we flip a coin five times, what's the probability the first flip was a tail, if we know exactly…

A:

Q: Exercise 9. Suppose that Z,, Z2,Z3 are independent N(0,1) random variables. (c) Compute P(Z? + Z3 +…

A: We want to find the probability.  Note: We want to find the probability by using standard normal…

Q: 1. Let X₁ and X₂ be any random variables, then V(X₁ + X₂) must be: A) greater than V(X₁) + V(X₂). B)…

A: Variance is the measure of dispersion which is used to determine the spread of the distribution.

Q: 8. 6. Say events A1, A2, . are almost disjoint if P(A; NAj) = 0, i+ j. Show for such events 80…

A:

Q: Let A, B, C, D and E be discrete random variable such that A is Binomial random variable with…

A:

Q: de

A: X and Y are  independent random variables each taking the values -1 or 1 with probability , P=12.…

Q: 1 in a simple random sanpling if 50 people, find the prob that less than 38  perrcent of our sample…

A: Given : 40 %people are afraid of dogs , p = 0.4     1) in a simple random sampling if 50 people,…

Q: Q.6| Suppose that I have a coin for which P(H)=p and P(T)=1-p. I toss the coin 5 times. a) What is…

A: Given: P(h)=p P(T)= 1-p  suppose a coin is tossed 5 times a) what is the probability that the out…

Q: solve and explain. step by step solution will be very helpful too.thank you

A: a)   (P[X&lt;3])- The probability that X is less than 3 Given that X is uniformly distributed in the…

Q: a.b.c

A: Standard normal distribution:The standard normal distribution is a special case of normal…

Q: 1. Let the random variable X denote a natural number selected at random from 1 to 25 inclusive. Find…

A: According to the provided information, X denotes a natural number selected at random from 1 to 25…

Q: Sunday 4 10 Monday 24 20 Tuesday 21 20 Wednesday 18 20 Thursday 22 20 Friday 28 20 Saturd Observed…

A: Given : The Hypothesis are :

Q: If X, and X, are two independent random variables, then Px, + x, (@) = Øx, (@) Øx, (@) %3D

A:

Q: A random variable has CDF given by Ai {A 1 = 0,1,2 1 i = 3 if A = 0.1, then what is po? F; =

A:

Q: 5) Two events X and Y are such that P(X) = 4, P(Y) = = P(Y) = — and P(XIY) = - ³1. Find the…

A: GivenP(X)=47, P(Y)=12 and P(X|Y)=34

Q: Question 4 Let X be a random variable with AX) 0, EX) 0.6. { if x 1 Answer (1) and (2): (1) If X,…

A:

Q: a) Let X₁, X₂, X3,..., X, be a random sample of size n from population X. Suppose that X~N(0, 1) Σ=1…

A: Given  X~N(θ,1)

Q: City University has both a men's and women's lacrosse team. Both teams play their games vs. other…

A: A and B are two events such that P(A),P(B)&gt;0. The conditional probability of A given that B has…

Q: Q1. a) In a group of 80 students, 50 have a laptop (A), 30 have a tablet (B) and 3 have both a…

A: Given Information: Total number of students = 80 50 have a laptop (A) 30 have a tablet (B) 3 have…

Q: Suppose X is a random variable with E(X) = 0 and Var(X) = 2. What is E(X2 )? a). 1 b). 2 c). 3 d).…

A: