Question

2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a Bernoulli random variable. That is, X takes the values 0 or 1, and P(X 1-p. a. Compute E(X) b. Show that Var(X)-p(1-p). c. Compute E(X).

0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
2. For a discrete random variable X, with CDF F(X), it is possible to show that...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Let X be a discrete random variable with PMF

    Let X be a discrete random variable with PMF(a) Find P(X ≤ 9). (b) Find E[X] and Var(X). (c) Find MX(t), where t < ln 3.

  • he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x)...

    he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable

  • An input source for an electrical system is modeled by a discrete random variable X where...

    An input source for an electrical system is modeled by a discrete random variable X where X takes on a value at random from sample space S={1, 2, 3, and 4} volts with corresponding CDF of this random variable, F X ( x ) = {0.2, 0.3, 0.7, and 1.0}. (a) Find P X ( x ), the PMF of this random variable. (b) Let event B be P [ X < 3]. Find P[B]. (c) Find the expected value...

  • 4- Let Y = X, where X is a discrete uniform integer random variable in the...

    4- Let Y = X, where X is a discrete uniform integer random variable in the range [-4,4). a) What is the PMF of the variable X? b) What is the PMF of the variable Y? c) Draw the PMF of the variables X, and Y. d) Draw the CDF of the variables X, and Y. e) What is the expected value of the random variables X and Y? f) What is the variance of the random variables X and...

  • 5. Let X be a discrete random variable. The following table shows its possible values r...

    5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of

  • Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be...

    Q6 (4pt) Let X be a discrete uniform random variable over {1,2,...,6} and let Y be a Bernoulli random variable with parameter 1/2 such that X, Y are independent. (1) Find the PMF of the random variable Z, where Z XY. (2) Compute the third moment of Z, that is, E[z2

  • Additional Problem 3. If X is a continuous random variable having cdf F, then its median...

    Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1. Additional Problem 6. Let X be a continuous random variable with pdf (a) Compute E(X), the mean of X (b) Compute Var(X), the variance of X. (c) Find an expression for Fx(r),...

  • 3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2...

    3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2 for 0.2 for x=3 Pg(x)=〈 0.1 for x=4 0.25 for x=5 0.15 for x=6 otherwise a) (10 points) Find E[X] b) (10 points) Find Var(X) c) Let Y-* I. (15 points) Find E[Y] II. (15 points) Find Var(Y) X-HX 4. Consider a discrete random variable X with E [X]-4x and Var(X) = σ. Let Y a. (10 points) Find E[Y] b. (20 points) Find...

  • (a) Below is the CDF for a discrete random variable, X if x 1 1/2 if...

    (a) Below is the CDF for a discrete random variable, X if x 1 1/2 if 1 x< 2 if 2 x 3 7/8 if 3 x 4 F(x) = 3/4 2 1 if nx <n+1. Describe the probability 2n In general, note that for any positive integer n, F(x) distribution of X by finding P(X 1), P(X = 2), P(X positive integer n, and describe an experiment that would result in this random variable X. 3), and the general...

  • 5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10...

    5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10 x < 0; Fx(x) = { 0.5 0<x< 1; (1 x > 1. Is X a discrete random variable or continuous random variable? (b) Consider a CDF of a random variable Y, 1 < 0; Fy(y) = { ax + b 0 < x < 1; 11 x >1, for some constant a and b. If Y is a continuous random variable, then what...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT