Question

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.

(d) Find the expected value of X

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
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 ).
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.
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 ).
7. For the random variable x with probability density function: f(x) = {1/2 if 0 <...
7. For the random variable x with probability density function: f(x) = {1/2 if 0 < x< 1, x − 1 if 1 ≤ x < 2} a. (4 points) Find the CDF function. b. (3 points) Find p(x < 1.5). c. (3 points) Find P(X<0.5 or X>1.5)
Let the probability density function of the random variable X be f(x) = { e ^2x...
Let the probability density function of the random variable X be f(x) = { e ^2x if x ≤ 0 ;1 /x ^2 if x ≥ 2 ; 0 otherwise} Find the cumulative distribution function (cdf) of X.
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).
Suppose that X is a continuous random variable with a probability density function that is a...
Suppose that X is a continuous random variable with a probability density function that is a positive constant on the interval [8,20], and is 0 otherwise. a. What is the positive constant mentioned above? b. Calculate P(10?X?15). c. Find an expression for the CDF FX(x). Calculate the following values. FX(7)= FX(11)= FX(30)=
X is a continuous random variable with the cumulative distribution function F(x)   = 0               when...
X is a continuous random variable with the cumulative distribution function F(x)   = 0               when x < 0 = x2              when 0 ≤ x ≤ 1 = 1               when x > 1 Compute P(1/4 < X ≤ 1/2) What is f(x), the probability density function of X? Compute E[X]
Probability density function of the continuous random variable X is given by f(x) = ( ce...
Probability density function of the continuous random variable X is given by f(x) = ( ce −1 8 x for x ≥ 0 0 elsewhere (a) Determine the value of the constant c. (b) Find P(X ≤ 36). (c) Determine k such that P(X > k) = e −2 .
1. f is a probability density function for the random variable X defined on the given...
1. f is a probability density function for the random variable X defined on the given interval. Find the indicated probabilities. f(x) = 1/36(9 − x2);  [−3, 3] (a)    P(−1 ≤ X ≤ 1)(9 − x2);  [−3, 3] (b)    P(X ≤ 0) (c)    P(X > −1) (d)    P(X = 0) 2. Find the value of the constant k such that the function is a probability density function on the indicated interval. f(x) = kx2;  [0, 3] k=
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT