Question

Consider the following exponential probability density function. f(x) = (1)/(5)e−x/5    for x ≥ 0 (a) Write...

Consider the following exponential probability density function.

f(x) = (1)/(5)e−x/5    for x ≥ 0

(a) Write the formula for P(x ≤ x0).

(b) Find P(x ≤ 3). (Round your answer to four decimal places.)

(c) Find P(x ≥ 5). (Round your answer to four decimal places.)

(d) Find P(x ≤ 7). (Round your answer to four decimal places.)

(e) Find P(3 ≤ x ≤ 7). (Round your answer to four decimal places.)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
f (x, y) =(x+y)/(5(5 + 2)) is a joint probability density function over the range 0...
f (x, y) =(x+y)/(5(5 + 2)) is a joint probability density function over the range 0 < x < 5 and 0 < y < 2. Find V (X). Please report your answer to 3 decimal places.
Let X be a random variable with probability density function f(x) = {3/10x(3-x) if 0<=x<=2 .........{0...
Let X be a random variable with probability density function f(x) = {3/10x(3-x) if 0<=x<=2 .........{0 otherwise a) Find the standard deviation of X to four decimal places. b) Find the mean of X to four decimal places. c) Let y=x2 find the probability density function fy of Y.
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.
1. Find k so that f(x) is a probability density function. k= ___________ f(x)= { 7k/x^5...
1. Find k so that f(x) is a probability density function. k= ___________ f(x)= { 7k/x^5 0 1 < x < infinity elsewhere 2. The probability density function of X is f(x). F(1.5)=___________ f(x) = {(1/2)x^3 - (3/8)x^2 0 0 < x < 2 elsewhere   3. F(x) is the distribution function of X. Find the probability density function of X. Give your answer as a piecewise function. F(x) = {3x^2 - 2x^3 0 0<x<1 elsewhere
1. Decide if f(x) = 1/2x2dx on the interval [1, 4] is a probability density function...
1. Decide if f(x) = 1/2x2dx on the interval [1, 4] is a probability density function 2. Decide if f(x) = 1/81x3dx on the interval [0, 3] is a probability density function. 3. Find a value for k such that f(x) = kx on the interval [2, 3] is a probability density function. 4. Let f(x) = 1 /2 e -x/2 on the interval [0, ∞). a. Show that f(x) is a probability density function b. . Find P(0 ≤...
Let X be a continuous random variable with the probability density function f(x) = C x,...
Let X be a continuous random variable with the probability density function f(x) = C x, 6 ≤ x ≤ 25, zero otherwise. a. Find the value of C that would make f(x) a valid probability density function. Enter a fraction (e.g. 2/5): C = b. Find the probability P(X > 16). Give your answer to 4 decimal places. c. Find the mean of the probability distribution of X. Give your answer to 4 decimal places. d. Find the median...
a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent...
a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent random variable following an identical distribution f(x):=e^(-x) if x>0, calculate the moment generating function of 2X+3Y b) If X follows a bernoulli(0.5), and Y follows a Binomial(3,0.5), and if X and Y are independent, calculate the probability P(X+Y=3) and P(X=0|X+Y=3)
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....
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)
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