The lifetime in months of a transistor in a certain application is random with probability density function: f(x) = {0.4e^-0.4x, x>0 0, x<0

a. Compute the mean lifetime.

b. Compute the standard deviation of the lifetimes.

c. Compute the cumulative distribution function of the lifetime.

d. Compute the probability that the lifetime will be less than 6 months.

e. Compute the 60^th percentile of the lifetime.

Explained below.

Step-by-step explanation:

The probability density function of lifetime in months of a transistor in a certain application is:

The probability density function suggests that the random variable X follows a exponential function with parameter λ = 0.4.

(a)

Compute the mean lifetime as follows:

Thus, the mean lifetime is 2.5 months.

(b)

Compute the standard deviation of the lifetimes as follows:

Thus, the standard deviation of the lifetimes is 2.5 months.

(c)

The cumulative distribution function of the lifetime is:

(d)

Compute the probability that the lifetime will be less than 6 months as follows:

Thus, the probability that the lifetime will be less than 6 months is 0.9093.

(e)

Compute the 60th percentile of the lifetime as follows:

Thus, the 60th percentile of the lifetime is 2.3 months.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet