Solution Found!
Applet Exercise When we discussed the ? 2 distribution in
Chapter 4, Problem 86E(choose chapter or problem)
Problem 86E
Applet Exercise When we discussed the χ 2 distribution in this section, we presented (with justification to follow in Chapter 6) the fact that if Y is gamma distributed with α = n/2 for some integer n, then 2Y/β has a χ 2 distribution. In particular, it was stated that when α = 1.5 and β = 4, W = Y /2 has a χ 2 distribution with 3 degrees of freedom.
a Use the applet Gamma Probabilities and Quantiles to find P(Y < 3.5).
b Use the applet Gamma Probabilities and Quantiles to find P(W < 1.75). [Hint: Recall that the χ2 distribution with ν degrees of freedom is just a gamma distribution with α = ν/2 and β = 2.]
c Compare your answers to parts (a) and (b).
Questions & Answers
QUESTION:
Problem 86E
Applet Exercise When we discussed the χ 2 distribution in this section, we presented (with justification to follow in Chapter 6) the fact that if Y is gamma distributed with α = n/2 for some integer n, then 2Y/β has a χ 2 distribution. In particular, it was stated that when α = 1.5 and β = 4, W = Y /2 has a χ 2 distribution with 3 degrees of freedom.
a Use the applet Gamma Probabilities and Quantiles to find P(Y < 3.5).
b Use the applet Gamma Probabilities and Quantiles to find P(W < 1.75). [Hint: Recall that the χ2 distribution with ν degrees of freedom is just a gamma distribution with α = ν/2 and β = 2.]
c Compare your answers to parts (a) and (b).
ANSWER:a
Calculation:
Applet calculates right hand tail probability P(Y > 3.5) = 0.62588
P(Y < 3.5) = 1- P(Y > 3.5) = 1- 0.62588 = 0.37412