5. Let X be a random variable whose density is given by the formula Sca? if x e (0, 2) f(x) = otherwise. (a) Find c. (b) Let Y be the integer part of X, i.e., Y = 0 if 0 < X < 1 and Y = 1 if 1 < X < 2. Let Z be the fractional part of X, i.e., Z = X-Y. Find the correlation between Y and Z.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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5. Let X be a random variable whose density is given by the formula
cx? if x E (0, 2)
f (x) =
otherwise.
(a) Find c.
(b) Let Y be the integer part of X, i.e., Y = 0 if 0 < X < 1 and Y = 1 if 1<X < 2.
Let Z be the fractional part of X, i.e., Z = X -Y. Find the correlation between Y and Z.
1
Transcribed Image Text:5. Let X be a random variable whose density is given by the formula cx? if x E (0, 2) f (x) = otherwise. (a) Find c. (b) Let Y be the integer part of X, i.e., Y = 0 if 0 < X < 1 and Y = 1 if 1<X < 2. Let Z be the fractional part of X, i.e., Z = X -Y. Find the correlation between Y and Z. 1
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