Given the following discrete probability distribution 1 Dete

Given the following discrete probability distribution

1) Determine the probability that x will be at least one(Please show me how you did it)=

2) Determine the standard deviation(Please show work) =

Solution

1.

x will be at least 1 if x = 2 or x = 4.

Thus, we just add P(2) and P(4),

P(at least 1) = 0.30 + 0.20 = 0.50 [ANSWER]

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2.

As

s = sqrt[Sum(x^2 P(X)] - (Sum (x P(x))^2]

Then

X   P(X)   x^2 P(x)   xP(x)
-2   0.5   2   -1
2   0.3   1.2   0.6
4   0.2   3.2   0.8
      
Sum(x^2 P(x))   Sum(xP(x))
6.4      0.4

Thus,

s = 2.497999199 [ANSWER]