1. [4 points] Consider a random variable X whose probability distribution function is given by 0.4...
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...
5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.
6. The distribution law of random variable X is given -0.4 |-0.2 |0 0.1 0.4 0.3 0 0.6 0.2 Pi Find the variance of random variable X. nrohahility density function is:
5. Consider a random variable X whose probability mass function is given by 0.1 ifx0.1 0.3 ifx2p p(x)p ifx 3 0 otherwise (a) What is p? (b) Compute P(1.9 S IXI s 3) (c) What is F(p)? What is F(2)? What is F(F(3))? (Here F() denote the cdf for X) d) What is P(2X-3s 41X 2 2.0)? (e) Compute Var(X) ( Compute E(F(p(X))
2. (-13 Points) DETAILS TANFIN12 8.3.002. The probability distribution of a random variable x is given. MY NOTES 12 -2 0 2 4 PCX = ) 0.3 0.1 0.2 0.2 0.2 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation The probability distribution of a random variable X is given. 1 View 2 3 4 P(X = x) 0.3 0.4 0.2 0.1 Compute the mean, variance, and standard deviation...
5.Consider a discrete random variable X with the probability mass function xp(x) Consider Y-g(X) 0.2 0.4 0.3 0.1 a)Find the probability distribution of Y b) Find the expected value of Y, E(Y) Does μ Y equal to g(μx)? 4
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
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
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. Here is the probability distribution for a random variable x: Value of X Probability 0.4 0.6 a. (4 pts) Find the mean and the standard deviation of this distribution. Show all work. b. (4 pts) Let Y 3X -2. Find the mean and the standard deviation of the distribution of Y Show all work and any rules you use c.(4 pts) Now let 2 3x2-2, Find the distribution of Z by completing the table below Value of Z Probability...