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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.
Write functions to solve the following problems:
- Leap Year Calculator (25 points)
Write a fuction isLeapYear with a parameter of type int named year.
The parameter needs to be greater than or equal to 1 and less than or equal to 9999.
If the parameter is not in that range return False.
Otherwise, if it is in the valid range, calculate if the year is a leap year and return True if it is a leap year, otherwise return False.
Tip: To determine whether a year is a leap year, follow these steps:
1. If the year is evenly divisible by 4, go to step 2. Otherwise, go to step 5.
2. If the year is evenly divisible by 100, go to step 3. Otherwise, go to step 4.
3. If the year is evenly divisible by 400, go to step 4. Otherwise, go to step 5.
4. The year is a leap year (it has 366 days). The method isLeapYear needs to return True.
5. The year is not a leap year (it has 365 days). The method isLeapYear needs to return False
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.
Determination of charge/mass ratio of electron using narrow fine beam tube experiment objective
Determination of charge/mass ratio of electron using narrow fine beam tube apparatus
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.
Determination of charge/mass ratio of electron using narrow fine beam tube full experiment
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)
#339914 on Dec 2023