Verify that the following function is a probability mass function, and determine the requested probabilities.
f(x) = (3x+4)/50, x = 0, 1, 2, 3, 4
Is the function a probability mass function? (yes/no)
Give exact answers in form of fraction.
(a) P(X = 4) = ?
(b) P(X ≤ 1) = ?
(c) P(2 ≤ X < 4) = ?
(d) P(X > -10) = ?
Given that,
f(x) = (3x+4)/50, x = 0, 1, 2, 3, 4
Therefore,
f(0) = [ (3 * 0) + 4]/50 = 4/50 = 0.08
f(1) = [ (3 * 1) + 4]/50 = 7/50 = 0.14
f(2) = [ (3 * 2) + 4]/50 = 10/50 = 0.20
f(3) = [ (3 * 3) + 4]/50 = 13/50 = 0.26
f(4) = [ (3 * 4) + 4]/50 = 16/50 = 0.32
Here, all f(xi) >= 0 and
Therefore, it is a proper probability mass function.
a) P(X = 4) = f(4) = 0.32
b) P(X <= 1) = f(0) + f(1) = 0.08 + 0.14 = 0.22
P(X <= 1) = 0.22
c) P(2 <= X < 4) = f(2) + f(3) = 0.20 + 0.26 = 0.46
P(2 <= X < 4) = 0.46
d) P(X > -10) = 1 - P(X <= -10) = 1 - 0 = 1.00
P(X > -10) = 1.00
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