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The lifespan of a car battery is approximately normally distributed, with mean equivalent to 4 years and a standard deviation of 5 years. What is the probability that a random sample of 25 car batteries would have an expected lifespan of (i) more than 6 years? (ii) at least 3 years but less than 7 years?
Let A and B are the bivariate continuous random variables. The joint probability density function is given by 𝑓(𝑎, 𝑏) = { 𝑎 2𝑏𝑥 0 < 𝑎 < 3, 0 < 𝑏 < 2; 0 otherwise. (i) Determine the value of x for which the function can serve as a joint probability density function. (ii) Find the marginal density function of B. (iii) Find 𝑓(𝑎 < 1|𝑏 = 1)
Define the joint probability distribution function of the bivariate random variables U and V if (i) U and V are discrete bivariate random variables, (ii) U and V are continuous bivariate random variables.
A coin is tossed three times. If Z is a random variable giving the number of heads obtained, (i) find the probability distribution of Z. (ii) what is the expected value of Z?
Consider a random experiment with sample space S. Explain the random variable as a function by using an example of rolling a dice twice and the sum of the numbers that turn up is recorded.
A particular female student has a mean height of 155 centimeters and a standard deviation of 20 centimeters, whilst a particular male student has a mean height of 170 centimeters and a standard deviation of 15 centimeters. What is the probability that a random sample of 36 female students will have a mean height lower than the mean height of 16 male students by at least 12.5 centimeters?
Large Consignments of computer components are inspected for defectives by means of a sampling system. Ten components are examined and the lot is to be rejected if two or more are found to be defective. If a consignments contains exactly 10% defectives. Find the probability of the consignment by using the technique of Binomial probability distribution that the consignment is: i) Accepted ii) Rejected
i) Between $1,320 and $970
ii) Under $1,400
iii) Over $1,290
b) An achievement test was administered to a class of 20,000 students. The mean score was 80 and the standard deviation was 11. If Lingard scored 72 in the test, how many students did better than him?
Retirement age(x)| 55 | 61| 52| 65| 70 |45 |60 |
Death age(y)| 60 |70 |88 |90 |62 | 50 | 77|
i) Calculate the Pearson correlation coefficient and interpret
ii) From a regression equation of the form y=α+βX+ε, where y is the retirement age, X is age at which one dies and ε, estimate the values for the constant and slope of the regression and interpret.
iii) Predict the age at which one will die if the person retires at age 78.
iv) Calculate the coefficient of determination and interpret.
X| 0 | 1| 2 | 3 | 4| 5|
Freq| 15| 24| 8| 6| 10| 4|
i) Use the table above to construct cumulative frequency and relative cumulative frequencies for the distribution
ii) Estimate the mean deviation
