Question

The strength X of a certain material is such that its distribution is found by X...

The strength X of a certain material is such that
its distribution is found by X = eY, where Y is N(10, 1).  Find the cdf and pdf of X, and compute P(10, 000 <
X < 20, 000). Note: F(x) = P(X ≤ x) = P(eY ≤ x) =
P(Y ≤ ln x) so that the random variable X is said to have
a lognormal distribution.

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
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf)...
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf) f. Consider the random variable Y = X?b a for a > 0 and real b. (a) Let G(x) = P(Y x) denote the cdf of Y . What is the relationship between the functions G and F? Explain your answer clearly. (b) Let g(x) denote the pdf of Y . How are the two functions f and g related? Note: Here, Y is...
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 the random variable X have pdf f(x) = x^2/18; -3 < x < 3 and...
Let the random variable X have pdf f(x) = x^2/18; -3 < x < 3 and zero otherwise. a) Find the pdf of Y= X^2 b) Find the CDF of Y= X^2 c) Find P(Y<1.9)
Suppose X is a random variable with pdf f(x)= {c(1-x) 0<x<1 {0 otherwise where c >...
Suppose X is a random variable with pdf f(x)= {c(1-x) 0<x<1 {0 otherwise where c > 0. (a) Find c. (b) Find the cdf F (). (c) Find the 50th percentile (the median) for the distribution. (d) Find the general formula for F^-1 (p), the 100pth percentile of the distribution when 0 < p < 1.
Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and...
Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables. Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.
Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and...
Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables. Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.
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.
For each of the random quantities X,Y, and Z, defined below (a) Plot the probability mass...
For each of the random quantities X,Y, and Z, defined below (a) Plot the probability mass function PMS (in the discrete case) , or the probability density function PDF (in the continuous case) (b) Calculate and plot the cumulative distribution function CDF (c) Calculate the mean and variance, and the moment function m(n), and plot the latter. The random quantities are as follows: X is a discrete r.q. taking values k=0,1,2,3,... with probabilities p(1-p)^k, where p is a parameter with...
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).
1. Let X be a random variable with PDF f(x) = C*absolute value(x), -1 <= x...
1. Let X be a random variable with PDF f(x) = C*absolute value(x), -1 <= x <= 1 A. Find the constant and plot the PDFof X. Identify P(X > 0.5) in the plot. B. Determine and plot the CDF of X. Identify P(X > 0.5) in the plot. C. Compute E(X^2 + X + 1).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT