Consider a population that is described by a random variable

Consider a population that is described by a random variable that takes the values 0.2 and 1.7 with probabilities 0.8 and 0.2 respectively 09. If a single sample is drawn at random from this population find the probability that its value will exceed 0.6. 10. If two samples are drawn independently at random from this population, find the (exact) probability that their average value will exceed 0.6 11. If 100 samples are drawn independently at random from this population, estimate the probability that their average value will exceed 0.6.

Solution

1)

0.2/1 = 0.2

2)

0.2/2 = 0.1

I divided by 2 because you have 2 sample

3)

0.2/100=0.002

I divided by 100 because you have 100 samples