Math

Let X be a standard normal random variable. Let Y be a continuous random variable such that
fY|X(y|x)=1/√2π−−exp(−(y+2x)^2/2).


Find E[Y|X=x] (as a function of x, in standard notation) and E[Y].

E[Y|X=x]=
unanswered

E[Y]= unanswered

Compute Cov(X,Y).

Cov(X,Y)= unanswered

The conditional PDF of X given Y=y is of the form
α(y)exp{−quadratic(x,y)}


By examining the coefficients of the quadratic function in the exponent, find E[X∣Y=y] and Var(X∣Y=y).

E[X∣Y=y]=
unanswered

Var(X∣Y=y)=

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. So if we look at the formula, fX|Y(x|y) ~ N(-2x,1), so
    E[Y|X=x] = -2x
    E[Y] = 0

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. The rest I'm not sure:
    cov(X,Y) = 0
    E[X|Y=y] = -y/2

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  3. Cov(X,Y)= -2
    E[X∣Y=y]= -2/5*y
    Var(X∣Y=y)= 1/5

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  4. E[Y|X=x] = -2x
    E[Y] = 0
    Cov(X,Y)= -2
    E[X∣Y=y]=-y/2
    Var(X∣Y=y)=1/16

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  5. why the cov(X,Y) = -2

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  6. E[Y|X=x] = -2x
    E[Y] = 0
    Cov(X,Y)= -2
    E[X∣Y=y]=-y/2
    Var(X∣Y=y)=1/4

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  7. E[Y|X=x] = -2x
    E[Y] = 0
    Cov(X,Y)= -2
    E[X∣Y=y]=-2y/5
    Var(X∣Y=y)=1/5

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. probability

    Problem 4. Gaussian Random Variables Let X be a standard normal random variable. Let Y be a continuous random variable such that fY|X(y|x)=12π−−√exp(−(y+2x)22). Find E[Y|X=x] (as a function of x , in standard notation)

  2. Probability

    Let X be a standard normal random variable. Let Y be a continuous random variable such that fY|X(y|x)=1/√2π*exp(−(y+2x)^2/2). Find E[Y|X=x] (as a function of x, in standard notation) and E[Y]. unanswered Compute Cov(X,Y).

  3. STATISTICS

    Consider a binomial random variable where the number of trials is 12 and the probability of success on each trial is 0.25. Find the mean and standard deviation of this random variable. I have a mean of 4 and a standard deviation

  4. Probability

    Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X . In case of Tails, we let Y=-X Is Y normal? (1 option is

  1. statistics

    Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). P(z -1.0) P(z -1.0) P(z -1.5) P(z -2.5) P(-3 < z 0)

  2. probability

    Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let 𝑋 and 𝑌 be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)𝑌 . Find the probability

  3. math 115

    Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation 25. Find the value of x so that the area under the normal curve between ì and x is approximately 0.4798 and the

  4. Probability

    Let X be a continuous random variable, uniformly distributed on some interval, and let Y = aX + b. The random variable will be a continuous random variable with a uniform distribution if and only if (choose one of the following

  1. statistics

    Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value less than 44.

  2. Probability

    1.Let 𝑋 and 𝑌 be two binomial random variables: a.If 𝑋 and 𝑌 are independent, then 𝑋+𝑌 is also a binomial random variable b.If 𝑋 and 𝑌 have the same parameters, 𝑛 and 𝑝 , then 𝑋+𝑌 is a binomial

  3. stats

    Let z be a random variable with a standard normal distribution, P(-1.9

  4. Elementary statistics

    Nine apples, four of which are rotten, are in a refrigerator. Three apples are randomly selected without replacement. Let the random variable x represent the number chosen that are rotten. Construct a table describing the

View more similar questions or ask a new question.