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The density function of the thickness of a conducive coating in micrometers is f(x) =
600x^−2
for 100 < x < 120.
a) Determine the mean and variance of the coating thickness.
b) If the coating costs $0.50 per micrometer of thickness on each part, what is the
average cost of the coating per part?
Suppose that contamination particle size (in micrometers) can be modeled as f(x) =
2x^−3
for x > 1. Determine the mean and standard deviation of X.
5. The maximum patent life for a new drug is 17 years. Subtracting the length of time
required by the FDA for testing and approval of the drug provides the actual patent life
of the drug – that is, the length of time that a company has to recover research and
development costs and make profit. Suppose the distribution of the lengths of patent life
for new drugs is as shown here:
x 3 4 5 6 7 8 9 10 11 12 13
f(x) 0.03 0.05 0.07 0.10 0.14 0.20 0.18 0.12 0.07 0.03 0.01
a) Find the expected number of years of patent life for a new drug.
b) Find the standard deviation of x.
c) Find the probability that x falls into the interval μ ± 2σ.
4. You can insure a $50,000 diamond for its total value by paying a premium of D dollars. If
the probability of theft in a given year is estimated to be 0.01, what premium should the
insurance company charge if it wants the expected gain to equal $1000?
3. Suppose that X has a discrete uniform distribution on the integers 0 through 9.
Determine the mean, variance, and standard deviation of the random variable Y = 5X
and compare to the corresponding results for X.
Seven students went on a diet in an attempt to lose weight, with two of them losing weight while all the others added weight. Is the diet is an effective way to losing weight α=1% (5mks)
2. A fire-detection device uses three-temperature-sensitive cells acting independently of
one another in such a manner that any one or more can activate the alarm. Each cell has
a probability p = 0.8 of activating the alarm when the temperature reaches 100° or
higher. Let X represent the number of cells activating the alarm when the temperature
reaches 100°. Find:
a) the probability distribution of X;
b) the expected value; and
c) the variance for the random variable X.
1. Marketing estimates that a new instrument for the analysis of soil samples will be very
successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1,
respectively. The yearly revenue associated with a very successful, moderately
successful, or unsuccessful is $10 million, $5 million, and $1 million, respectively. Let the
random variable X denote the yearly revenue of the product. Determine:
a) the mass function of X;
b) the mean of X; and
c) the variance of X.
A random sample of size 36 was taken from a population distributed as Nμ,3.92.The value of the sample x was 15.6. i. Find a 90% confidence interval for μ. (5mks)
It is believed that value of μ is 17. Use your confidence interval to comment on this belief.(2mks)
1.Solve the differential equation (2𝐷2 + 5𝐷 + 2)𝑦 = 𝑒-1/ 2 x
2. Solve the differential equation (𝐷3 − 3𝐷2 + 4𝐷 − 2)𝑦 = 𝑐𝑜𝑠𝗑.
#339914 on Dec 2023