Suppose a random variable X has a probability density function as shown in img1.jpg. a) Find the value of k that makes this a probability density function b) Find P(0.4 ≤ X ≤ 1). c) Find P(X ≤ 0.4 | X ≤ 0.8) d) Find F(b) = P(X ≤ b) and sketch the graph of this function.

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Suppose a random variable X has a probability density function as shown in img1.jpg.

a) Find the value of k that makes this a probability density function

b) Find P(0.4 ≤ X ≤ 1).

c) Find P(X ≤ 0.4 | X ≤ 0.8)

d) Find F(b) = P(X ≤ b) and sketch the graph of this function.

a Find the value of k that makes this a probabil-
ity density function.
b Find P (0.4 <X< 1).
c Find P (X < 0.4|X< 0.8).
d Find F (b) = P (X < b) and sketch the graph
of this function.
Transcribed Image Text:a Find the value of k that makes this a probabil- ity density function. b Find P (0.4 <X< 1). c Find P (X < 0.4|X< 0.8). d Find F (b) = P (X < b) and sketch the graph of this function.
kx(1 – x) 0sxs1
f(x)
%3D
elsewhere
Transcribed Image Text:kx(1 – x) 0sxs1 f(x) %3D elsewhere
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