Question

The probability distribution function for the random variable X, the lead content in a liter of...

The probability distribution function for the random variable X, the lead content in a liter of gasoline is: (a) Prove that f(x) IS a probability distribution function (b) Find the expected value of lead content in a liter of gasoline (c) Find the standard deviation of the lead content in a liter of gasoline (d) Find the equation for the cumulative distribution function of X f(x) = 12.5x – 1.25, 0.10 < x < 0.50 0, elsewhere

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
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 ).
The random variable X has probability density function: f(x) = ke^(−x) 0 ≤ x ≤ ln...
The random variable X has probability density function: f(x) = ke^(−x) 0 ≤ x ≤ ln 2 0 otherwise Part a: Determine the value of k. Part b: Find F(x), the cumulative distribution function of X. Part c: Find E[X]. Part d: Find the variance and standard deviation of X. All work must be shown for this question. R-Studio should not be used.
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....
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.
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 .
For probability density function of a random variable X, P(X < a) can also be described...
For probability density function of a random variable X, P(X < a) can also be described as: F(a), where F(X) is the cumulative distribution function. 1- F(a) where F(X) is the cumulative distribution function. The area under the curve to the right of a. The area under the curve between 0 and a.
A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 +...
A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 + e−x ) −1 , −∞ < x < ∞. (i) Find the probability density function (pdf) of X. (ii) Roughly, take 10 points in the range of x (5 points below 0 and 5 points more than 0) and plot the pdf on these 10 points. Does it look like the pdf is symmetric around 0? (iii) Also, find the expected value of X.
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.
Suppose that the probability mass function for a discrete random variable X is given by p(x)...
Suppose that the probability mass function for a discrete random variable X is given by p(x) = c x, x = 1, 2, ... , 9. Find the value of the cdf (cumulative distribution function) F(x) for 7 ≤ x < 8.
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤...
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤ x < ∞ 0 otherwise } for some λ > 0. a. Compute the cumulative distribution function F(x), where F(x) = Prob(X < x) viewed as a function of x. b. The α-percentile of a random variable is the number mα such that F(mα) = α, where α ∈ (0, 1). Compute the α-percentile of the random variable X. The value of mα will...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT