Question

Partially correct answer. Your answer is partially correct. Try again. Suppose that f left-parenthesis x right-parenthesis equals 1.5 x squared for negative 1 less-than x less-than 1. Determine the following probabilities: a) Upper P left-parenthesis 0 less-than Upper X right-parenthesis equalsEntry field with correct answer .5 b) Upper P left-parenthesis 0.5less-than Upper X right-parenthesis equalsEntry field with correct answer .4375 (Round the answer to 3 decimal places.) c) Upper P left-parenthesis negative 0.5 less-than-or-equal-to Upper X less-than-or-equal-to 0.5 right-parenthesis equalsEntry field with correct answer .125 (Round the answer to 3 decimal places.) d) Upper P left-parenthesis Upper X less-than negative 2 right-parenthesis equalsEntry field with correct answer 0 e) Upper P left-parenthesis Upper X less-than 0 or Upper X greater-than negative 0.5 right-parenthesis equalsEntry field with correct answer 1 f) Determine x such that Upper P left-parenthesis x less-than Upper X right-parenthesis equals 0.05. Entry field with incorrect answer .46415 (Round the answer to 3 decimal places.)

Answer 1

Answer:

a. 0.5

b. 0.4375

c. 0.125

d. 0

e. 1

f. 0.9655

Solving

Step-by-step explanation:

$given f(x)=\left \{ {{1.5x^{2} } \atop {0}} \right.$

for -1 ≤ x ≤ 1

a.

probability of P(0<X)

$\int\limits^1_0 {f(x) } \, dx \\x = 1.5x^{2} \\\int\limits^1_0 {1.5x^{2} } \, dx$

$1.5\int\limits^1_0 {x^{2} } \, dx$

when we integrate we have

$1.5[x^{2+1} ]/3$

$= \frac{1.5}{3} \\= 0.5$

b. probability of 0.5<x<1

$=\int\limits^1_ {0.5} 1.5x^{2} \, dx$

$\frac{7}{16} = 0.4375$

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