Question

In: Statistics and Probability

Let x be the number of bicycles owned by families in Canada, for which the probability...

Let x be the number of bicycles owned by families in Canada, for which the probability distribution is as follows:

x 0 1 2 3 ________________________

p(x) .1 .3 .55 .05

a. What is the mean and standard deviation of x?

b. Show the sampling distribution of x̄ for random samples of N=2 measurements drawn from the probability distribution of x.

c.Determine whether or not x̄ is an unbiased estimator of μ

d. An ideal point estimator should be consistent. What does this mean?

Solutions

Expert Solution

d.) An ideal point estimator should be consistent means that the estimator should be unbiased and variance of estimator should tend to 0 for large sample sizes. That means on increasing the sample size, the precision of estimator is maximum.


Related Solutions

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X...
Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows. X Frequency 1 3 2 3 3 7 4 13 5 13 6 1 Find: Sample Mean, Standard Deviation, Relative Frequency and Cumulative Relative Frequency, First and Third Quartiles, What percent of the students owned at least five pairs? (Round your answer to one decimal place.), 40th Percentile and 90th Percentile.
Shown below are the number of trials and success probability for some Bernoulli trials. Let X...
Shown below are the number of trials and success probability for some Bernoulli trials. Let X denote the total number of successes. n = 6 and p = 0.3 Determine ​P(x=4​) using the binomial probability formula. b. Determine ​P(X=4​) using a table of binomial probabilities. Compare this answer to part​ (a).
Let X be the number of heads and let Y be the number of tails in...
Let X be the number of heads and let Y be the number of tails in 6 flips of a fair coin. Show that E(X · Y ) 6= E(X)E(Y ).
Let x be the number of courses for which a randomly selected student at a certain...
Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below: x 1 2 3 4 5 6 7 p(x) .05 .03 .09 .26 .37 .16 .04 (a) What is P(x = 4)? P(x = 4) = (b) What is P(x 4)? P(x 4) = (c) What is the probability that the selected student is taking at most five courses? P(at...
What is the probability that the random variable X (which is the number of Heads from...
What is the probability that the random variable X (which is the number of Heads from flipping a coin 5 times) is equal to 0?
In the binomial probability distribution, let the number of trials be n = 4, and let...
In the binomial probability distribution, let the number of trials be n = 4, and let the probability of success be p = 0.3310. Use a calculator to compute the following. (a) The probability of three successes. (Round your answer to three decimal places.) (b) The probability of four successes. (Round your answer to three decimal places.) (c) The probability of three or four successes. (Round your answer to three decimal places.)
Let x be the number of different research programs, and let y be the mean number...
Let x be the number of different research programs, and let y be the mean number of patents per program. As in any business, a company can spread itself too thin. For example, too many research programs might lead to a decline in overall research productivity. The following data are for a collection of pharmaceutical companies and their research programs. x 10 12 14 16 18 20 y 1.9 1.4 1.6 1.4 1.0 0.7 Complete parts (a) through (e), given...
Independent trials, each of which is a success with probability p, are successively performed. Let X...
Independent trials, each of which is a success with probability p, are successively performed. Let X denote the first trial resulting in a success. That is, X will equal k if the first k −1 trials are all failures and the kth a success. X is called a Geometric random variable (google it). Determine the moment generating function of X.
The probability for a family having x dogs is given by: Number of Dogs, x Probability...
The probability for a family having x dogs is given by: Number of Dogs, x Probability of x, P(X=x) 0 .3 1 .4 2 .2 3 .1 Find the expected number of dogs that a family will have. Round to the nearest tenth.
Cosider x+y independent trials with success probability p. Let J be the number of total successes...
Cosider x+y independent trials with success probability p. Let J be the number of total successes in the x+y trials and X be the number of success in first x trial find the expectation of X
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT