Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density a.Verify if itis a valid density function. b.Find P[(X, Y) ∈A], where A = {(x, y) | 0 < x < ½, ¼ < y < ½. c.Find the marginal density g(x). d.Find the marginal density h(y). e.Find the conditional density f(x|y). f.Find the conditional density f(y|x). g.Find P(Y > 1| X = ½). h.Find P(X > ½ | Y = 1). i.Determine if the random variables are statistically independent.
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density a.Verify if itis a valid density function. b.Find P[(X, Y) ∈A], where A = {(x, y) | 0 < x < ½, ¼ < y < ½. c.Find the marginal density g(x). d.Find the marginal density h(y). e.Find the conditional density f(x|y). f.Find the conditional density f(y|x). g.Find P(Y > 1| X = ½). h.Find P(X > ½ | Y = 1). i.Determine if the random variables are statistically independent.
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.
Chapter4: Calculating The Derivative
Section4.4: Derivatives Of Exponential Functions
Problem 53E
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Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density
a.Verify if itis a valid density
b.Find P[(X, Y) ∈A], where A = {(x, y) | 0 < x < ½, ¼ < y < ½.
c.Find the marginal density g(x).
d.Find the marginal density h(y).
e.Find the conditional density f(x|y).
f.Find the conditional density f(y|x).
g.Find P(Y > 1| X = ½).
h.Find P(X > ½ | Y = 1).
i.Determine if the random variables are statistically independent.
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