08 - (a Compute these using the table on page 201 Then...

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BTRY/STSCI 4080 Homework # 8 Due Date: 11/11/10 Problem numbers beginning with P (e.g., P1) denote problems from the “PROB- LEMS” section; those beginning with T (e.g., T1) denote problems taken from the “THEORETICAL EXERCISES” section. 1. Ross: p 225, P7: (a) Find a,b as requested. (b) Compute P ( X > 2 / 3) and P ( A ), where A = { X < 0 . 2 } ∪ { X > 0 . 7 } . 2. Ross: p 225, P11 3. Ross: p 225, P12 4. Ross: p 225, P17 5. Ross: p 225, P20: (a) Write down the correct binomial probabilities. Then, numerically compute these prob- abilities using the pbinom function in R . Report your results and include your R code. (b) Write down the appropriate continuity-corrected approximation to the probabilities in
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Unformatted text preview: (a). Compute these using the table on page 201. Then, verify these calculations using the pnorm function in R . Report all results and include your R code. 6. Ross: p 226, P31 7. Ross: p 226, P32 8. Ross: p 228, T11 9. Ross: p 228, T29 10. Let β > 0 and suppose X is a continuous random variable with pdf f ( x ) = 4 β 3 √ π x 2 e-x 2 β 2 I ( x > 0) . (a) Show that E ( X ) = 2 β √ π . (b) Find V ar ( X ). (c) Let Y ∼ Gamma( 3 2 , 1). Show that P ( X ≤ a ) = P ( Y ≤ a 2 β 2 ) for any a > 0. (d) Use the pgamma function in R to compute P ( X ≤ 2 3 ) when β = 1....
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