If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...

Question

Question

If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...

If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random variable with p2 = 3/4, are those two random variables necessarily independent?

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Add a comment

Answer 2

Similar Homework Help Questions

X1 and X2 are discrete random variables (and are independent) with probability functions: p1(x1) = 1/3...

X1 and X2 are discrete random variables (and are independent) with probability functions: p1(x1) = 1/3 for x1 = −2 ,−1 , 0 p2(x2) = 1/2 for x2 = 1, 6 Let Y = X1 + X2 a). Find the MGF of X1, X2 and Y b). USE MGFS derived in part a) to determine the probability mass function of Y. Note: MGFs in part a) must be used to determine the pmf of Y in part b)
1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/...

1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/ x , if 0 < x < 1, 0 < y < x f(x, y) =0, otherwise . Find the covariance of the random variables X and Y . 2.Let X1 be a Bernoulli random variable with parameter p1 and X2 be a Bernoulli random variable with parameter p2. Assume X1 and X2 are independent. What is the variance of the random variable Y...
Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof u...

Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof using the de finition of distribution function that the the distribution function of Z =Y Xit(1-Y)X2 is F = pF14(1-p)F2 Don't use generatinq moment functions, characteristic functions) Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter...

Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y;...

Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y; be the partial sums, i.e., Y1 = X1, Y2 = X1 + X2, Y3 = X1 + X2 + X3. 1. What is the distubution for each Yį, i = 1, 2, 3? 2. What is the expected value for Y1 + Y2 +Yz? 3. Are Yį and Y2 independent? Explain it by computing their joint P.M.F. 4. What is the variance of Y1...
Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y :=...

Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y := X1 + X2 and U := X1X2. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y . (You may wish to use {X2 = i}, i = 0,1, as a partition and apply the total probability formula.) (b) Compute the mean and variance of Y in two different ways, one is through the pdf of Y...
Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2,...

Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The joint probability mass function of these two random variables are given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15 0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions fX1 (s) and fX2 (t). b. What is the expected values of X1...

Q2 Suppose X1, X2, ..., Xn are i.i.d. Bernoulli random variables with probability of success p....

Q2 Suppose X1, X2, ..., Xn are i.i.d. Bernoulli random variables with probability of success p. It is known that p = ΣΧ; is an unbiased estimator for p. n 1. Find E(@2) and show that p2 is a biased estimator for p. (Hint: make use of the distribution of X, and the fact that Var(Y) = E(Y2) – E(Y)2) 2. Suggest an unbiased estimator for p2. (Hint: use the fact that the sample variance is unbiased for variance.) Xi+2...
Let X1 and X2 be random variables, not necessarily independent. Show that E [X1 + X2]...

Let X1 and X2 be random variables, not necessarily independent. Show that E [X1 + X2] = E [X1] + E [X2]. You may assume that X1 and X2 are discrete with a joint probability mass function for this problem, while the above inequality is true also for continuous random variables.
3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...

3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What is the distribution of N? (b) Find the conditional distribution of (X1, X2, X3) | N. (c) Now let N, X1, X2, X3, be random variables such that N~ Poisson(A), (X1, X2, X3) | N Trinomial(N; pi,p2.ps) where pi+p2+p3 = 1. Find the unconditional distribution of (X1, X2, X3). 3. (25 pts.) Let X1,...

Let X1 d = R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, deﬁne Y := X1 + X2 and U := X1X2. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y . (You may wish to...

Let X1 d = R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, deﬁne Y := X1 + X2 and U := X1X2. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y . (You may wish to use {X2 = i}, i = 0,1, as a partition and apply the total probability formula.) (b) Compute the mean and variance of Y in two diﬀerent ways, one is through the pdf of...

If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...

Homework Answers

Add Answer to:
If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...

Post as a guest

Earn Coins

X1 and X2 are discrete random variables (and are independent) with probability functions: p1(x1) = 1/3...

1. Suppose X,Y are random variables whose joint pdf is given by f(x, y) = 1/...

Let Xi and X2 independent random variables, with distribution functions F1, and F2, respectively Let Y a Bernoulli random variable with parameter p. Suppose that Y, X1 and X2 are independent. Proof u...

Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y;...

Let X1 d= R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, define Y :=...

Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2,...

Q2 Suppose X1, X2, ..., Xn are i.i.d. Bernoulli random variables with probability of success p....

Let X1 and X2 be random variables, not necessarily independent. Show that E [X1 + X2]...

3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...

Let X1 d = R(0,1) and X2 d= Bernoulli(1/3) be two independent random variables, deﬁne Y := X1 + X2 and U := X1X2. (a) Find the state space of Y and derive the cdf FY and pdf fY of Y . (You may wish to...

If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...

Homework Answers

Add Answer to: If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...

Post as a guest

Earn Coins

Add Answer to:
If X1 is a Bernoulli random variable with P1 = 1/2 and X2 is Bernoulli random...