2 (a) The number of particles emitted per second by a radioactive source has a Poisson distribution with mean 20. Calculate the probabilities of

(i) 0 (ii) 1 (iii) 2 (iv) 3 or more emissions in a time interval of 1 second

(b) y 17 18 19 20 21 22 23 P (Y = y) 0.1 0.2 0.1 0.1 0.2 0.1 0.2

Calculate the standard deviation of the random variable Y above.

(c) There are 800 pupils in a school. Find the probability that exactly5 of them have their birthdays on 1 January, by using (????) B (800, 1/365) (????) Po (800/365)

(d) A continuous random variable, has a probability density function, f(x), given by

1 ????????????1≤????≤???? ????(????) = {????2

0 ????????h????????????????????????

Height(m)

1.55- 1.59

1.60- 1.64

1.65- 1.69

1.70- 1.74

1.75- 1.79

1.80- 1.84

1.85- 1.89

1.90- 1.94

1.95- 1.99

JULY, 2021

A random sample of 100 observations is taken from this distribution, and the mean, ????, is found. Write

Find (i) the mean, μ (ii) the variance,σ2, of this distribution down the distribution of ????.

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Customer: 3 Consider the table of values below

Age(x) 21 23 24 27 30 32 Mark (y) 100 80 95 85 75 95 (a) Calculate the Spearman’s rank correlation for the data and explain the value.

(b) You are given the data set on the following table:

Y 24 32 40 50 60 72 82 X 11 15 19 24 29 35 40

(i) fit the regression line for these two variables (where Y is the dependent variable and X is the independent variable)

(ii) Interpret the intercept of the linear regression line (iii) interpret the slope of the linear regression line (iv) calculate the response if X is 30.