Answer:
a. 0.5
b. 0.4375
c. 0.125
d. 0
e. 1
f. 0.9655
Solving
Step-by-step explanation:
[tex]given f(x)=\left \{ {{1.5x^{2} } \atop {0}} \right.\\[/tex]
for -1 ≤ x ≤ 1
a.
probability of P(0<X)
[tex]\int\limits^1_0 {f(x) } \, dx \\x = 1.5x^{2} \\\int\limits^1_0 {1.5x^{2} } \, dx[/tex]
[tex]1.5\int\limits^1_0 {x^{2} } \, dx[/tex]
when we integrate we have
[tex]1.5[x^{2+1} ]/3[/tex]
[tex]= \frac{1.5}{3} \\= 0.5[/tex]
b. probability of 0.5<x<1
[tex]=\int\limits^1_ {0.5} 1.5x^{2} \, dx[/tex]
[tex]\frac{7}{16} = 0.4375[/tex]
c. probability of p(-0.5≤X≤0.5)
I had difficulty using the math editor. ALmost ran out of time. please check the attachment for the solution to this.
the answer is 1/8 = 0.125
d. probability of x<-2 is equal to 0
e. p(x<0 or X>-0.5)
= p(X>-0.5) + p(x<0.5)
= 1-0.0625 + 0.0625
= 0.9375 + 0.0625
= 1
f.
we are to solve for P(x<X) = 0.05
= 0.9655
PLEASE CHECK ATTACHMENT FOR FULL CALCULATIONS
