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The number of automobile accidents a driver will be involved in during a one-year period is a random variable Y having a Poisson distribution with parameter X, where X depends on the driver. Suppose a driver is chosen at random from some population and hence X itself is a
continuous random variable with p.d.f f(x) , 0 < x < ∞
(a) Show that P(Y=k)= int o ^ infty P(Y=k|X=x)f(x)dx
(b) Suppose that x has an exponential distribution with mean 1/c where c is a
positive constant. Obtain the distribution of Y, hence find the expectation of Y.
The random variable X_{1} , X 2 ,.......,Xn , are independent and each has a poisson distribution with mean 1. Let Y=X 1 +X 2 +........+Xn . find the conditional distribution of X mathcal N given Y.
Consider Y, the number of successes in Mindependent Bernoulli trials each with success
probability X. Suppose that X itself is a r.v which is uniformly distributed over (1, 0)
(a) Find the p.m.f of Y and identify the distribution
(b) What is the mean and variance of Y.
The number of eggs X laid by an insect is known to have a binomial distribution with
parameter n and p.(0<p<1) . Each egg laid has a probability of hatching independently
of the development of any other eggs.
(a) Show that the number of eggs hatched has a binomial distribution
(b) What does this mean?
(c) What is the mean and variance of the number of eggs hatched?
An operation manager in charge of a company's manufacturing keeps track of the number of LED television in a day. Compute for the following data that represents the number of the LED television manufactured for the past three (3) weeks: 20,18,19,25,20,21,20,25,30,29,28,29,25,25,27,26,22. a. Construct frequency distribution (frequency,cumulative frequency, class boundaries and midpoint). In determining the classes of the data you will use (Rules #1). b. Compute for the mean,median and mode of the data using grouped data. c. Construct a stem and leaf of the data.
Given a sample of 100 projector bulbs from a company has a mean
length of life of 20.5 hours with a standard deviation of 1.6 hours, how do I find a 95% confidence interval for the average length of life of those bulbs and then interpret the results?
The mean gasoline consumption of 10 cars is 28 liters with a standard
deviation of 1.6 liters. Find the interval estimate using 95% confidence
interval.
average senior high annual costs of tuition fee for all private schools last year was php43,700,a random sample costs this year for 45 private schools indicated that the sample mean was php45,800 and a sample standard deviation was php5,600 at 0.01 level of significance is there sufficent evidence for conclude that the cost increased ?
C. Find the mean (𝝁𝑿), variance (𝝈𝑿 𝟐) and standard deviation (𝝈𝑿) of the sampling distribution of the means given the sample size, and the means and standard deviation of the population. Sample size n were randomly selected from the population
7. 𝑛 = 9
𝜇 = 5.3
𝜎 = 3
Mean:
Variance:
Standard Deviation:
8. 𝑛 = 11
𝜇 = 4.23
𝜎 = 5
Mean:
Variance:
Standard Deviation:
B. Find the mean (𝝁) variance (𝝈 2)and standard deviation (𝝈) of the population given the sample size, and the means and variances of the sampling distribution of the means. Sample size n were randomly selected from the population
4. 𝑛 = 5
𝜇𝑥 = 3
𝜎²𝑥 = 4.5
Mean:
Variance:
Standard Deviation:
5. 𝑛 = 7
𝜇𝑥 = 10
𝜎²𝑥 = 6
Mean:
Variance:
Standard Deviation:
