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.

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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