Question Solved1 Answer Let Y denote a random variable that has a Poisson distribution with mean λ = 6. (Round your answers to three decimal places.) (a) Find P(Y = 9). (b) Find P(Y ≥ 9). (c) Find P(Y < 9). (d) Find P(Y ≥ 9|Y ≥ 6).

8S1DTH The Asker · Probability and Statistics

Let Y denote a random variable that has a Poisson distribution with mean λ = 6. (Round your answers to three decimal places.)

(a) Find P(Y = 9).

(b) Find P(Y ≥ 9).

(c) Find P(Y < 9).

(d) Find P(Y ≥ 9|Y ≥ 6).

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&#160;Y&#160;denotes a random variable that has a Poisson distribution with mean&#160;&#955;&#160;= 6 The probability of&#160;Y=y is P(Y=y)=(lambda^(y)e^(-lambda))/(y!)=(6^(y)e^(-6))/(y!),quad y=0,1,dots (a) Find&#160;P(Y&#160;= 9). P(Y=9)=(6^(9)e^(-6))/(9!)=0.0688 ans: P(Y=9) = 0.069 (b) Find&#160;P(Y&#160;&#8805; 9). {:[P(Y >= 9)=1-P(Y < 9)],[=1-(P(Y=0)+P(Y=1)+dots+P(Y=8))],[=1-((6^(0)e^(-6))/(0!)+(6^(1)e^(-6))/(1!)+dots+(6^(8)e^(-6))/(8!))],[=1-(0.0025+0.0149+0.0446+0.0892+0.1339+0.1606+0.1606+0.1377+0.1033)],[=0.1528]:} ans:&#160;P(Y&#160;&#8805; 9) = 0.153 (c) Find&#160;P(Y&#160;&lt; 9) {:[P(Y < 9)=1-P(Y >= 9)],[=1-0.1528" from part "b],[=0. ... See the full answer