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. |
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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