Question

a.A radioactive source is emitting, on the average, one particle per minute. If counting continues for several hundred minutes, during which time the particles are emitted randomly, in what proportion of these minutes is to be expected that

i.There will be 2 or more particles emitted? (3 Marks)

ii.There will be 2 or more particles emitted in 2 minutes?(3 Marks)

b.The number of snakes found in each of 100 sampling quadrats in an area were as follows:

Number of snakes, s

0

1

2

3

4

5

8

15

f = frequency of s

69

18

7

2

1

1

1

1

Find the mean and variance of the number of snakes per sampling unit. Determine whether or not the data fit the Poisson distribution. (4 Marks)

c.Consider tossing 4 coins, which are properly balanced so that the probability of a head at each toss is . Let r be the number of heads resulting from the 4 tosses.

i.Construct the probability distribution for r. (4 Marks)

ii.Compute the expected value and variance for r. (2 Marks)

d.Persons suffering from a blood disease are found to have an abnormality in one particular chromosome. However, not all samples of this chromosome are abnormal, and in order to estimate the proportion of affected ones, 5 examples of this chromosome are examined from each of 120 patients, the number of affected one, r, being recorded for each patient. The results are tabulated below;

r

0

1

2

3

4

5

f = frequency

6

31

42

29

10

2

Estimate the proportion p of affected chromosomes and hence compute their variance. (4 Marks)

TOTAL [20 MARKS]