1 In Economics Education, there has been a significant focus on the gender mix of undergraduate programmes in Economics. You should define the true proportion of females within undergraduate economics programmes across the UK as p, where p is unknown. To investigate this, you have randomly sampled 50 individuals, and asked them their sex. Of the 50 individuals, 14 were female, and 36 were male. a) Write down the probability distribution function of a random variable X that takes the value 1 when an observation is female and 0 otherwise amongst economics students. b) When you randomly sample 50 individuals, this is equivalent to randomly sampling 50 observations, X; from the PDF defined in a). The number of females, in your sample, can be defined as: c) d) Calculate p Y = 1 == n 50 i=1 Write down the distribution of Y in terms of p. Hint: what distribution will Y follow? Calculate E (Y) and var (Y) as a function of p Xi n 1 X. What is the interpretation of p in this example?