STA4321-hw5-solns - Homework solution PDF

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= P (X ⩾ k | rainy)P (rainy) + P (X ⩾ k | dry)P (dry) n ( ) n ( ) ∑ ∑ n x n x p (1 − p2 )n−x p 1 (1 − p1 )n−x + (1 − α) =α x 2 x x=k

x=k

2

1

0!

= e−2.5 = 0.082085

3 ∑ e−2.5 (2.5)x x! x=0

=1−e

−2.5

e−2.5 (2.5)1 e−2.5 (2.5)2 e−2.5 (2.5)3 − − − = 0.2424239 3! 1! 2!

, λt =

p

p3 + 3p3 (1 − p) + 6p3 (1 − p)2

= p2 (1 + 2(1 − p) + 3(1 − p)2 )

=

1 + 2(1 − p) + 3(1 − p)2 1 + 3(1 − p) + 6(1 − p)2

Bin(7, 0.7)

= P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7) ( ) ( ) ( ) ( ) 7 7 7 7 6 1 5 2 4 3 0.77 0.7 0.3 + 0.7 0.3 + 0.7 0.3 + = 7 6 5 4 = 0.873964

P (X = 4) + P (X = 3) (7) 4 3 0.7 0.3 4 ( ) = (7 ) 4 0.33 + 7 0.73 0.34 0.7 4 3 0.2268945 = 0.7 = 0.2268945 + 0.0972405

x=0

e−5.2 (5.2)x 5.22 5.23 ) = 0.238 = e−5.2 (1 + 5.2 + + 6 x! 2...