Students arrive at a college cafeteria for lunch in batches

Students arrive at a college cafeteria for lunch in batches (or groups). The students in a group, K, is a random variable whose PMF is given by Determine the following: The numerical value of b The expected value of K The CDF of K. The variance of K.

Solution

a)

By normalization,

3b + 5b + 2b = 1

10b = 1

Thus,

b = 0.1 [ANSWER]

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b)

E(k) = Sum(k P(k)) = 2*0.3 + 3*0.5 + 4*0.2 = 2.9

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c)

P(k) = 0.3, k = 2
0.8, k = 3
1, k = 4 or more

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d)

Thus,      
      

Var(x) = E(x^2) - E(x)^2 =    0.49 [ANSWER]

x	P(x)	x P(x)	x^2 P(x)
2	0.3	0.6	1.2
3	0.5	1.5	4.5
4	0.2	0.8	3.2