In Minecraft, TNT produces rectangular craters when it blows up. It is known that the lengthL (in metres) and width W (in metres) of the rectangle are discrete random variables with jointprobability function f(l, w) = klw², for w = 1,2, l = 1, 2, 3, where k is a positive constant.Find the value of k.Determine and justify if L and W are independent.Find the conditional probability function of W given L = 2.Let A be the area of the rectangle formed, A = L × W. Find the range and probabilityfunction of A.

here as per guidelines i have calculated 3 subparts plz repost for remaining here given joint…

Answered: Find the value of k. Determine and…

Find the value of k. Determine and justify if L and W are independent. Find the conditional probability function of W given L = 2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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Question

In Minecraft, TNT produces rectangular craters when it blows up. It is known that the length
L (in metres) and width W (in metres) of the rectangle are discrete random variables with joint
probability function f(l, w) = klw², for w = 1,2, l = 1, 2, 3, where k is a positive constant.
Find the value of k.
Determine and justify if L and W are independent.
Find the conditional probability function of W given L = 2.
Let A be the area of the rectangle formed, A = L × W. Find the range and probability
function of A.

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