5. Consider a random variable X whose probability mass function is given by 0.1 ifx0.1 0.3...
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...
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
1. [4 points] Consider a random variable X whose probability distribution function is given by 0.4 ifx=0 0.3 if3 0 elsewhere (I) find the value of k (2) find the mean of X (3) find the variance of X
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
2) Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X=1) =0.2, P(X=2) = 0.3, P(X=3) = 0.3, and P(X=4)= 0.1. A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated...
Let X be the random variable whose probability density function is f(x) = ce−5x , if x > 0 f(x)=0, if otherwise (a) Find c. (b) Find P(1 ≤ 2X − 1 ≤ 9). (c) Find F(2) where F denotes the c.d.f. of X. (d) Write an equation to find E[3X2 + 15]. You do not have to evaluate it.
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
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).
2. The random variable X has probability density function f given by f(x) 0 otherwise. (a) Is X continuous or discrete? Explain. (b) Calculate E(X). (c) Calculate Var(2X 9).
х 1 4 5 4. The probability distribution of a random variable X is given below -4 3 P(X=x) 0.1 0.2 0.3 0.2 a) Find E(X) 0.2 b) Find Var(X)