Determine the correlation for the following joint probability distribution 1 1 2 4 3 4 5 7 fw(X.y) 1/8 1/4 1/2 1/8
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- А. Identify if the following are valid probability distributions for a discrete random variable X. a. X 3 0.4 4 P(X) 0.1 0.5 b. 1 4. 16 P(X) 0.40 0.50 -0.10 0.20 C. -2 -1 1 P(X) 0.15 0.25 0.10 0.50 d. 1 4 P(X) 5 25 e. 4 1 3. P(X) 36 18 36 12 5S 315 215AnConsider the joint probability distribution of X and Y: x = 0 x = 1 P(y) y = 0 y = 1 P(x) 0.5 0.2 0.7 0.1 0.2 0.3 0.6 0.4 1 What is pxr (rounded to four decimal places)?
- 1. A random variable x has the probability distribution as follows: 1. 2 3. 4 P(x) 1/15 k/15 k/5 4/15 k/15 a. Find k. b. Construct a probability histogram to descibe P(x).A probability distribution function is modeled by the following X-Y cartesian graph: 15k 长 6 7 12 Determine the following: 1. Probability density function for the intervals defined on the graph. 2. Expected value of X. 3. Variance of X. I 4. P(X<5) 5. P(25.1.1 WP X 1.0 1.5 1.5 2.5 3.0 y 1 23+ 4 5 fxy(x, y) 1/4 1/8 1/4 1/4 1/8 5.2.2 WP Consider the joint distribution in Exercise 5.1.1. Determine the following: a. Conditional probability distribution of Y given that X = 1.5 b. Conditional probability distribution of X that Y = 2 c. E(Y | X = 1.5) d. Are X and Y independent?Pavan.98If X is normally distributed with mean 0 and variance 1, what is the probability density function of X2 ?1. Determine the constant c so that the function p(x) = 0(x) defines the probability den- sity for a random variable {. Then find the cumulative distribution function and the mean of {. %3DSuppose that X follows a binomial distribution with n = 100 and p = 0.1. If F(x) is the cumulative distribution function of the Standard Normal distribution. Then using the Normal approximation, the probability P(X = 16) is obtained by O a. F(2.17) - F(1.83) O b. F(1.83) - F(2.17) O c. F(16.5) + F(15.5) O d. F(17.0) - F(15.0)Find the mean and variance of the following probability distributions.13. Answer the following for the probability distribution 1 f(x) = (2x + 1) (2x + 1) X= 0, 1, 2, 3 16 a. Find the mean and the variance. μ = b. EX²-4X+6) 0²=SEE MORE QUESTIONS