Question

suppose that the lifetime of a transistor is a gamma random variable x with mean of 24 weeks and standard deviation of 12 weeks. what is the probability that the transistor will last between 12 and 24 weeks?

Answer 1

Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer 2

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma($\alpha ,\beta$)

E(X)= $\alpha \beta$                 $\beta$= $12^{2}/24$=6 weeks

V(x)= $\alpha \beta ^{2}$                $\alpha$=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, $\alpha$, $\beta$, False)

P($12\leq X\leq 24$)

P($12/6\leq G\leq 24/6$)

P($2\leq G\leq 4$)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4