Hey I need help with these question can anyone help me with

Hey I need help with these question, can anyone help me with these please

1. Given F(x) = 2x+3, Find f(x) for 0 x 2.

2. What is the probability of getting atleast 2 heads in 3 independent trials of tossing a fair coin?

3. Given that F(x) = 2e^xand x > 0 Find E(x)

4. What is the probability of getting a second head on the 5^th trial of 5 independent trials of tossing a fair coin?

Solution

1.

F(x) = 2x + 3

however, we note that the maximum value of F(x) is 1, and the minimum is 0. Thus, getting where the boundaries are,

2x + 3 = 0 --> = -3/2
2x + 3 = 1 --> -1

Thus,

F(x) = 2x + 3, -3/2<=x<=-1
0, otherwise

As f(x) = F\'(x),

f(x) = 2, -3/2<=x<=-1
0, otherwise [ANSWER]

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