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3 years ago

Use the order of operations to simplify the expression. PLEASE EXPLAIN

Mathematics

1 answer:

lilavasa [31]3 years ago

6 0

Its 23, you do the times first then add.
3x5=15
15+8=23

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On any given day, mail gets delivered by either Alice or Bob. If Alice delivers it, which happens with probability 1/4 , she doe

Troyanec [42]

Answer:

(a) The value of fₓ (9.5) is 0.125.

(b) The value of fₓ (10.5) is 0.50.

Step-by-step explanation:

Let X denote delivery time of the mail delivered by Alice and Y denote delivery time of the mail delivered by Bob.

It i provided that:

$X\sim U(9, 11)\\Y\sim U(10, 12)$

The probability that Alice delivers the mail is, p = 1/4.

The probability that Bob delivers the mail is, q = 3/4.

The probability density function of a Uniform distribution with parameters [a, b] is:

$f(x)=\left \{ {{\frac{1}{b-a};\ a, b>0} \atop {0;\ otherwise}} \right.$

The probability density function of the delivery time of Alice is:

$f(X_{A})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[9, 11]} \atop {0;\ otherwise}} \right.$

The probability density function of the delivery time of Bob is:

$f(X_{B})=\left \{ {{\frac{1}{b-a}=\frac{1}{2};\ [a, b]=[10, 12]} \atop {0;\ otherwise}} \right.$

(a)

Compute the value of fₓ (9.5) as follows:

For delivery time 9.5, only Alice can do the delivery because Bob delivers the mail in the time interval 10 to 12.

The value of fₓ (9.5) is:

$f_{X}(9.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times0)\\=\frac{1}{8}\\=0.125$

Thus, the value of fₓ (9.5) is 0.125.

(b)

Compute the value of fₓ (10.5) as follows:

For delivery time 10.5, both Alice and Bob can do the delivery because Alice's delivery time is in the interval 9 to 11 and that of Bob's is in the time interval 10 to 12.

The value of fₓ (10.5) is:

$f_{X}(10.5)=p.f(X_{A})+q.f(X_B})\\=(\frac{1}{4}\times \frac{1}{2})+(\frac{3}{4}\times\frac{1}{2})\\=\frac{1}{8}+\frac{3}{8}\\=0.50$

Thus, the value of fₓ (10.5) is 0.50.

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3 years ago