Question

Random variables X and Y are jointly and uniformly distributed in a triangular area with vertices (0,0), (1,0) and (0,1) as shown in the figure below; the value of the joint PDF is 2 in the shaded area and zero outside it. Calculate E[X]. 1/8 1/6 1/2 1/3 0.4 1/4

          Random variables X and Y are jointly and uniformly distributed in a triangular area with vertices (0,0), (1,0) and (0,1) as shown in the figure below; the value of the joint PDF is 2 in the shaded area and zero outside it.
Calculate E[X].
1/8
1/6
1/2
1/3
0.4
1/4

Random variables X and Y are jointly and uniformly distributed in a triangular area with vertices (0,0), (1,0) and (0,1) as shown in the figure below; the value of the joint PDF is 2 in the shaded area and zero outside it.
Calculate E[X].
1/8
1/6
1/2
1/3
0.4
1/4

Added by Michael F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

11/07/2022

Step 1

The area of a triangle can be calculated using the formula A = 0.5 * base * height. In this case, the base and height of the triangle are both 1 unit. So, the area of the triangular region R is A = 0.5 * 1 * 1 = 0.5 square units. Show more…

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Random variables X and Y are jointly and uniformly distributed in a triangular area with vertices (0,0), (1,0), and (0,1) as shown in the figure below. The value of the joint PDF is 2 in the shaded area and zero outside it. Calculate E[X]: