7.Give an example of a discrete-type random variable with an infinite mean. (Give the p.m.f., and show that the mean is infinite.)
7.Give an example of a discrete-type random variable with an infinite mean. (Give the p.m.f., and...
Give an example of a discrete or continuous random variable X (by giving the p.m.f. or p.d.f.) whose cumulative distribution function F(x) satisfies F(n)=1-1/n! Thank you very much! Exercise 3.40. Give an example of a discrete or continuous random variable X p.d.f.) whose the cumulative distribution function F(x) (by giving the p.m.f satisfies F(n)1 - i for each positive integer n or
The joint probability mass function (p.m.f.) of the discrete random variables X and Y is given by 11/4 1/2 20 1/4 (a) Are X and Y independent? (b) Compute P(XY 1) and P(2X Y >1) (c) Find P(y > 1 | X = 1) (d) Compute the conditional p.m. f. of X given Y = 1
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
** Question 1: Consider the following discrete probability distribution. The mean of this random variable is 3.75. x 0 1 2 5 P(X=x) 0.10 0.70 a) Find the missing values for P(X=1) and P(X=2) Hint: you will need to use two equations here, and substitution. This should be familiar from high school mathematics. The two equations you will need are for the mean of a discrete random variable and that the sum of all the probabilities equals 1. - please...
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (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. (d) Compute the mean and the variance of X.
5. Suppose X is a discrete random variable that has a geometric distribution with p= 1. a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X> 6). [5] c. Use Chebyshev's Inequality to estimate P(X>6). [5] t> 0 6. Let be the probability density function of the continuous 0 t< 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that...
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
Let X be a discrete random variable that follows a Poisson distribution with = 5. What is P(X< 4X > 2) ? Round your answer to at least 3 decimal places. Number
Please solve this. 8.18 A discrete random process is defined by where φ is a uniform rndom variable in the range of-π to π. (a) Sketch a typical sample function of X b) Are its mean and variance constants (i.e., independent of k)7 (e) Is X Je] stationary (d) Is it mean ergodic? 8.18 A discrete random process is defined by where φ is a uniform rndom variable in the range of-π to π. (a) Sketch a typical sample function...