If X follows the following probability distribution: .20 2 <X <3 f (x) = .60 3...

If X follows the following probability distribution:

.20 2 <X <3
f (x) = .60 3 <X <4
.20 4 <X <5
0 for other X’s

a. Calculate the cumulative probability function of X and make a reasonable graphical representation. (15 pts)
b. Calculate the expected value of X and the Variance of X. (15 pts)
c. Calculate the probability that X is between 2.40 and 3.80. (10 pts)
d. Calculate the percentile of 70 percent. (10 pts)
e. If g (x) = 10-3x, find the expected and variance of g (x).

Expert Solution

orchestra answered 2 years ago

If the joint probability distribution of X and Y f(x, y) = (x + y)/2

If the joint probability distribution of X and Y f(x, y) = (x + y)/2, x=0,1,2,3; y=0,1,2, Compute the following a. P(X≤2,Y =1) b. P(X>2,Y ≤1) c. P(X>Y) d. P(X+Y=4)

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 &nbsp

a. For the following probability density function: f(X)= 3/4 (2X-X^2 ) 0 ≤ X ≤ 2 = 0 otherwise find its expectation and variance. b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8 =0 , compute mean of X and mean of Y. Find correlation coefficient r , estimate y for x =3 and x for y = 3.

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0...

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0 1 2 y 0 0.12 0.08 0.06 1 0.04 0.19 0.12 2 0.04 0.05 0.3 Find the followings: E(Y)= Var(X)= Cov(X,Y)= Correlation(X,Y)=

5. Suppose that X and Y have the following joint probability distribution: f(x,y) x 2 4...

5. Suppose that X and Y have the following joint probability distribution: f(x,y) x 2 4 y 1 0.10 0.15 2 0.20 0.30 3 0.10 0.15 Find the marginal distribution of X and Y. Find the expected value of g(x,y) = xy2 or find E(xy2). Find (x and (y. Find Cov(x,y) Find the correlations ρ(x,y) 3. The length of life X, in days, of a heavily used electric motor has probability density function Find the probability that the motor has...

Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2....

Consider a distribution with the density function f(x) = x^2/3 for −1 ≤ x ≤ 2. (a) Randomly pick a sample of size 20 from this distribution, find the probability that there are 2 to 4 (inclusive) of these taking negative values. (b) Randomly pick an observation X from this distribution, find the probability that it is between 1.2 and 1.4, i.e., P (1.2 < X < 1.4). (c) Randomly pick a sample of size 40 from this distribution, and...

Determine the correlation for the following joint probability distribution: x 2 4 2 4 y 3...

Determine the correlation for the following joint probability distribution: x 2 4 2 4 y 3 4 5 6 fx,y(x,y) 1/8 1/4 1/2 1/8 a. Correlation = 0.6387 b. Correlation = 0.0377 c. Correlation = 0.3737 d. Correlation = 0.8023

Suppose X follows a Gamma distribution with parameters α, β, and the following density function f(x)=...

Suppose X follows a Gamma distribution with parameters α, β, and the following density function f(x)= [x^(α−1)e^(−x/ β)]/ Γ(α)β^α . Find α and β so that E(X)= Var(X)=1. Also find the median for the random variable, X.

Given the following table: Probability X Y 20% 15% 30% 60% 25% 18% 20% 30% 20%...

Given the following table: Probability X Y 20% 15% 30% 60% 25% 18% 20% 30% 20% Calculate a) the covariance of X and Y, and b) the correlation coefficient. Select one: a. a) -20.64% b) -0.90 b. a) -20.18% b) -0.88 c. a) -17.89% b) -0.78 d. a) -19.20% b) -0.84 e. a) -18.35% b)-0.80

Let be the following probability density function f (x) = (1/3)[ e ^ {- x /...

Let be the following probability density function f (x) = (1/3)[ e ^ {- x / 3}] for 0 <x <1 and f (x) = 0 in any other case a) Determine the cumulative probability distribution F (X) b) Determine the probability for P (0 <X <0.5)

For a newsvendor product the probability distribution of demand X (in units) is as follows: xi...

For a newsvendor product the probability distribution of demand X (in units) is as follows: xi 0 1 2 3 4 5 6 pi 0.05 0.1 0.2 0.3 0.2 0.1 0.05 The newsvendor orders Q = 4 units. a) Derive the probability distributions and the cumulative distribution functions of lost sales as well as leftover inventory. b) Knowing that the expected total cost function is convex in the order quantity Q, demonstrate that Q = 4 gives the minimal expected...

Question