Question

b. The Joint density of c.r.v X and Y is given by $f(x,y) = \begin{cases} kx^2y, & 0 \le x \le 1, 0 \le y \le 1\\ 0, & \text{otherwise} \end{cases}$ Find, i. The value of k. (3 Marks) ii. $P(\frac{1}{2} \le x \text{ and } \frac{1}{2} \le y \le \frac{3}{4})$ (3 Marks) iii. Marginal distribution and mean of X. (5 Marks)

          b. The Joint density of c.r.v X and Y is given by
$f(x,y) = \begin{cases} kx^2y, & 0 \le x \le 1, 0 \le y \le 1\\ 0, & \text{otherwise} \end{cases}$
Find,
i. The value of k.
(3 Marks)
ii. $P(\frac{1}{2} \le x \text{ and } \frac{1}{2} \le y \le \frac{3}{4})$
(3 Marks)
iii. Marginal distribution and mean of X.
(5 Marks)

b. The Joint density of c.r.v X and Y is given by
f(x,y) = kx^2y, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
0, otherwise
Find,
i. The value of k.
(3 Marks)
ii. P((1)/(2)≤ x and (1)/(2)≤ y ≤(3)/(4))
(3 Marks)
iii. Marginal distribution and mean of X.
(5 Marks)

Added by Joanne R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Hoan Nguyen

07/09/2023

Step 1

To find the value of k, we need to integrate the joint density function over its entire range and set it equal to 1, since the joint density function must integrate to 1 over its support. The range of x is from 0 to 1, and the range of y is also from 0 to Show more…

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b. The joint density of the continuous random variables X and Y is given by (f_{X,Y}(x,y) = kxy) for (0 leq x leq 1) and (0 leq y leq 1), and (f_{X,Y}(x,y) = 0) otherwise. Find: i. The value of k. ii. (P(X leq y leq 3)). iii. The marginal distribution and mean of X. (3 Marks) (3 Marks) (5 Marks)