Question

Exercise 12.18. Sleeping schedule. A student gets at least 8 hours of sleep 45% of the nights, the sleeping schedule is independent from night to night. Let X1, X2, X3, X4 indicate whether the student gets at least 8 hours of sleep during the next four nights respectively. Let X = X1 + X2 + X3 + X4. Find the variance of X

Answer 1

P( at least 8 hour sleep ) = 0.45 ,

The number of nights out of 4 nights to get at least 8 hour sleep could be modelled as a binomial distribution such that:

Xi ~ Bernoulli(p=0.45)

X ~ Bin(n 4. p = 0.45)

The variance now is computed as:

σ2 = np(1-p) = 4 * 0.45 * (1-0.45) = 0.99

Therefore 0.99 is the required variance here.