Question

The current in a certain circuit as measured by an ammeter is
a continuous random variable X with the following density
function:

f(x) = {.75x + .2 | 3=

Answer 1

Hello,

a) see the image

f(3)=0.075*3+0.2=0.425
f(5)=0.075*5+0.2=0.575
f(4)=0.075*4+0.2=0.5
f(3.5)=0.4625
f(4.5)=0.5375



b) P(X<=4)=(0.425+0.5)/2 * 2=0.925
 How does .... I have not understood the question (X and x)
But P(X=4)=0

c)
P(3.5<=X<=4.5)=(0.4625+0.5375)/2*1=0.5
P(X<=4.5)=(0.425+0.5375)/2*(4.5-3)=0,721875
P(X<=3.5)=(0.425+0.4625)/2*  0.5=0,221875
Rem: P(3.5<=X<=4.5)=P(X<=4.5)-P(X<=3.5)=0.721875-0.221875=0.5

P(X=4.5)=0