Question 6: Let n 2 be an integer and let a1, a2, {1, 2, . . . ,n). Defin an be a permutation of the set e ao = 0 and an+1-0, and consider the sequence lo, a1, l2, l3, . . . , ,n, ln+1- A position i with 1-i-n is called awesome, if ai ai-1 and ai ai+1. In words, i is awesome if the value at position i is larger than both its neighboring values. For example, if n - 6 and the permutation is 2,5,4,3,1,6, we get the sequence value0 2 5 4 31 6 0 position012 In this case, the positions 2 and 6 are awesome, whereas the positions 1, 3, 4, and 5 are not awesome Consider a uniformly random permutation of the set {1,2, . n} and define the random variable X to be the number of awesome positions. Determine the expected value E(X) of the random variable X Hint: Use indicator random variables, Question 6: Let n 2 be an integer and let a1, a2, {1, 2, . . . ,n). Defin an be a permutation of the set e ao = 0 and an+1-0, and consider the sequence lo, a1, l2, l3, . . . , ,n, ln+1- A position i with 1-i-n is called awesome, if ai ai-1 and ai ai+1. In words, i is awesome if the value at position i is larger than both its neighboring values. For example, if n - 6 and the permutation is 2,5,4,3,1,6, we get the sequence value0 2 5 4 31 6 0 position012 In this case, the positions 2 and 6 are awesome, whereas the positions 1, 3, 4, and 5 are not awesome Consider a uniformly random permutation of the set {1,2, . n} and define the random variable X to be the number of awesome positions. Determine the expected value E(X) of the random variable X Hint: Use indicator random variables