2.13 Consider the discrete random variable defined by x 0 1 34 5 36 36 36...
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...
Discrete Random Variable. The random variable x has the discrete probability distribution shown here: x -2 -1 0 1 2 p(x) 0.1 0.15 0.4 0.3 0.05 Find P(-1<=x<=1) Find P(x<2) Find the expected value (mean) of this discrete random variable. Find the variance of this discrete random variable
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...
Consider a discrete random variable X with pmf x)-(1-p1 p. defined for x - 1, 2, 3,..The moment generating function for this kind of random variable is M(t)Pe 1-(1-P)et. (a) What is E(X)? O p(1-P) 1-P (a) What is Var(x)? 1-p p2 p(1-P) O p(1-P) o -p
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).
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...
2. Consider a discrete random variable X with mean u = 4.9 and probability distribution function p(x) given in the table below. Find the values a and b and calculate the variance o p(x) 0.25 5 6 0.35
A discrete-time random process X[k] is defined by k Y[k] = x[i] i=0 x[i] = { +2 with probability p -1 with probability 1 - P Determine the mean and variance of Y [k] for p = 0.48 and k = 4.
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
** 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...