20 pts total] Consider the random variable X with the following CDF shown below a. [04...
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...
Question 6 A random variable X has cdf χ20 Plotthe cdf and identif.,(x)-1-0.2~ a) Plot the cdf and identify the type of the random variable. b) Find the pdf of X. c) Calculate P[-4eX<-1], P(xS2], P(X=1], Pf2-K6], and P[X>10]. d) Calculate the mean and the variance of X. If the random variable X passes through a system with the following chara cteristic function: e) f) Find the pdf of Y. Calculate the mean and the variance of Y. Good Luck
consider random variable X with the CDF, F(x) shown. i) find the variance of X [V(X)] ii) calculate P(X=7 | X >= 6) 8 T 4 5 6 7 F(I) 0.15 0.15 0.20 0.23 0.74 1.00
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),...
2. The CDF of the continuous random variable V is 15 v (a) Determine the value of the constant c required to make this CDF continuous. (b) What is P(V > 4)? (c) What is fv(v)? d) Calculate E V] and Var(V)
2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| | denote the absolute value. (a) Find the PMF ofY (b) Find the CDF of Y (c) Find E[Y] and Var(Y] (d) Find P IYel Y 3] 2. Det X be a geometric random variable with mean S. Define a new random variable Y using the following function Y-11,-31 ifXcS 2 ifX25 Where| |...
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...
Consider the probability distribution shown for the random variable x found below. Complete part a through f. 0 x P(x) 3 0.4 4 0.2 6 0.2 12 0.2 a. Find = E(x) = 5.6 (Round to the nearest tenth as needed.) b. Find o =E[(x-1)2]. (Round to the nearest hundredth as needed.) c. Find o. o= (Round to four decimal places as needed.) d. Interpret the value you obtained for p. Choose the correct answer below. O A. The average...
Problem 6. Consider a random variable X whose cumulative distribution function (cdf) is given by 0 0.1 0.4 0.5 0.5 + q if -2 f 0 r< 2.2 if 2.2<a<3 If 3 < x < 4 We are also told that P(X > 3) = 0.1. (a) What is q? (b) Compute P(X2 -2> 2) (c) What is p(0)? What is p(1)? What is p(P(X S0)? (Here, p(.) denotes the probability mass function (pmf) for X) (d) Sketch a plot...
Problem(3) (6 points) Consider the random variable X whose density is given by p(z) - ksin(x) ST (a) (1 pt) Find the value k so that p(x) is a probability density function. (b) (3 pts) Find E(X) and E(X2) Var(X) and Var(-tX) (d) (2 pts) Find ơ2