Answer:
a) 0.96
b) 0.016
c) 0.018
d) 0.982
e) x = 2
Step-by-step explanation:
We are given with the Probability density function f(x)= 2/x^3 where x > 1.
<em>Firstly we will calculate the general probability that of P(a < X < b) </em>
P(a < X < b) =
=
=
{ Because
}
=
=
=
=
a) Now P(X < 5) = P(1 < X < 5) {because x > 1 }
Comparing with general probability we get,
P(1 < X < 5) =
=
= 0.96 .
b) P(X > 8) = P(8 < X < ∞) = 1/
- 1/∞ = 1/64 - 0 = 0.016
c) P(6 < X < 10) =
=
= 0.018 .
d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)
=
+ (1/
- 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982
e) We have to find x such that P(X < x) = 0.75 ;
⇒ P(1 < X < x) = 0.75
⇒
= 0.75
⇒
= 1 - 0.75 = 0.25
⇒
=
⇒
= 4 ⇒ x =
Therefore, value of x such that P(X < x) = 0.75 is 2.
For this do 5/8-1/2!! in order to do this, find the common denominator. this one is 16, so do: 10/16-8/16, and simplify!
Answer: 296 degrees
Step-by-step explanation:
Arc PRT is just the entire circumference - arc PT.
Since the 64 degree angle is a central angle, arc PT measures 64 degrees.
So arc PRT = 360 degree - 64 degree = 296 degrees.
Answer:
The complex number
has Cartesian form
.
Step-by-step explanation:
First, we need to recall the definition of
when
is a complex number:
.
Then,
. (I)
Now, recall the definition of the complex exponential:
.
So,

(we use that
.
Thus,

Now we group conveniently in the above expression:
.
Now, substituting this equality in (I) we get
.
Thus,

.