Question

2. The incomplete probability distribution table at the right is of the discrete random variable x...

2. The incomplete probability distribution table at the right is of the discrete random variable x representing the number of times people donate blood in 1 year. Answer the following:
x P(X=x)
(a) Determine the value that is missing in the table. (Hint: what are the requirements for a probability distribution?) 0 0.532
1 0.124
2 0.013
(b) Find the probability that x is at least 2 , that is find P(x ≥ 2). 3 0.055
4 0.129
5
(c) Find P(x ≤ 1).  Describe what the resulting value represents within the given context. 6 0.023
(d) Find the mean μ (expected value) and standard deviation σ of this probability distribution.

Homework Answers

Answer #1

a) Let the missing value be 'p'

Sum of probabilities = 1

0.532 + 0.124 + 0.013 + 0.055 + 0.129 + p + 0.023 = 1

p = 1 - 0.876

p = 0.124

b) P(x 2) = 0.013 + 0.055 + 0.129 + 0.124 + 0.023

= 0.344

c) P(x 1) = 0.532 + 0.124

= 0.656

d) Mean, = 0x0.532 + 1x0.124 + 2x0.013 + 3x0.055 + 4x0.129 + 5x0.124 + 6x0.023

= 1.589

Standard deviation, = [(0-1.589)2x0.532 + (1-1.589)2x0.124 + (2-1.589)2x0.013 + (3-1.589)2x0.055+ (4-1.589)2x0.129 + (5-1.589)2x0.124 + (6-1.589)2x0.023]1/2

= 2.034

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