Question

5. A continuous random variable ? has probability distribution function ?(?) , where ?(?) = ?(1...

5. A continuous random variable ? has probability distribution function ?(?) , where ?(?) = ?(1 − ? 2 ) ??? − 1 < ? < 1.

(a) Find the value of ?.

(b) Compute the expected value of the random variable ?.

(c) Find the variance of the random variable ?.

(d) Calculate the ?(? < 0)?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and...
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and 0 otherwise (a) Find the value c such that f(x) is indeed a density function. (b) Write out the cumulative distribution function of X. (c) P(1 < X < 3) =? (d) Write out the mean and variance of X. (e) Let Y be another continuous random variable such that  when 0 < X < 2, and 0 otherwise. Calculate the mean of Y.
3. (10pts) Let Y be a continuous random variable having a gamma probability distribution with expected...
3. (10pts) Let Y be a continuous random variable having a gamma probability distribution with expected value 3/2 and variance 3/4. If you run an experiment that generates one-hundred values of Y , how many of these values would you expect to find in the interval [1, 5/2]? 4. (10pts) Let Y be a continuous random variable with density function f(y) = 1 2 e −|y| , −∞ < y < ∞ 0, elsewhere (a) Find the moment-generating function of...
A continuous random variable X has pdf ?x(?) = (? + 1) ?^2, 0 ≤ ?...
A continuous random variable X has pdf ?x(?) = (? + 1) ?^2, 0 ≤ ? ≤ ? + 1, Where B is the last digit of your registration number (e.g. for FA18-BEE-123, B=3). a) Find the value of a b) Find cumulative distribution function (CDF) of X i.e. ?? (?). c) Find the mean of X d) Find variance of X.
6. A continuous random variable X has probability density function f(x) = 0 if x< 0...
6. A continuous random variable X has probability density function f(x) = 0 if x< 0 x/4 if 0 < or = x< 2 1/2 if 2 < or = x< 3 0 if x> or = 3 (a) Find P(X<1) (b) Find P(X<2.5) (c) Find the cumulative distribution function F(x) = P(X< or = x). Be sure to define the function for all real numbers x. (Hint: The cdf will involve four pieces, depending on an interval/range for x....
If the probability density function of a random variable X is ce−5∣x∣ , then (a) Compute...
If the probability density function of a random variable X is ce−5∣x∣ , then (a) Compute the value of c. (b) What is the probability that 2 < X ≤ 3? (c) What is the probability that X > 0? (d) What is the probability that ∣X∣ < 1? (e) What is the cumulative distribution function of X? (f) Compute the density function of X3 . (g) Compute the density function of X2 .
a) Suppose that X is a uniform continuous random variable where 0 < x < 5....
a) Suppose that X is a uniform continuous random variable where 0 < x < 5. Find the pdf f(x) and use it to find P(2 < x < 3.5). b) Suppose that Y has an exponential distribution with mean 20. Find the pdf f(y) and use it to compute P(18 < Y < 23). c) Let X be a beta random variable a = 2 and b = 3. Find P(0.25 < X < 0.50)
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0...
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0 < ? < 2. (a) Find the constant c. (b) Find the cumulative distribution function (CDF) of X. (c) Find P(X < 0.5), and P(X > 1.0). (d) Find E(X), Var(X) and E(X5 ).
Suppose that X1 and X2 are independent continuous random variables with the same probability density function...
Suppose that X1 and X2 are independent continuous random variables with the same probability density function as: f(x) = ( x 2 0 < x < 2, 0 otherwise. Let a new random variable be Y = min(X1, X2,). a) Use distribution function method to find the probability density function of Y, fY (y). b) Compute P(Y > 1). c) Compute E(Y )
Consider a continuous random variable X with the probability density function f X ( x )...
Consider a continuous random variable X with the probability density function f X ( x ) = |x|/C , – 2 ≤ x ≤ 1, zero elsewhere. a) Find the value of C that makes f X ( x ) a valid probability density function. b) Find the cumulative distribution function of X, F X ( x ).
1. A continuous random variable is normally distributed. The probability that a value in the distribution...
1. A continuous random variable is normally distributed. The probability that a value in the distribution is greater than 47 is 0.4004. Find the probability that a value in the distribution is less than 47. 2. A continuous random variable is normally distributed. The probability that a value in the distribution is less than 125 is 0.5569. Find the probability that a value in the distribution is greater than 125. 3. A random variable is normally distributed with mean 89.7...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT