True or false The solution to the inequality 5x+2<175x+2<17 is x<3x<3.

Suppose we roll a fair die and let X represent the number on the die. (a) Find the moment generating function of X. (b) Use the

Likurg_2 [28]

Answer:

(a) moment generating function for X is $\frac{1}{6}\left(e^{t}+e^{2 t}+e^{2 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$

(b) $\mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}$

Step-by step explanation:

Given X represents the number on die.

The possible outcomes of X are 1, 2, 3, 4, 5, 6.

For a fair die, $P(X)=\frac{1}{6}$

(a) Moment generating function can be written as $M_{x}(t)$ .

$M_x(t)=\sum_{x=1}^{6} P(X=x)$

$M_{x}(t)=\frac{1}{6} e^{t}+\frac{1}{6} e^{2 t}+\frac{1}{6} e^{3 t}+\frac{1}{6} e^{4 t}+\frac{1}{6} e^{5 t}+\frac{1}{6} e^{6 t}$

$M_x(t)=\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$

(b) Now, find $E(X) \text { and } E\((X^{2})$ using moment generating function

$M^{\prime}(t)=\frac{1}{6}\left(e^{t}+2 e^{2 t}+3 e^{3 t}+4 e^{4 t}+5 e^{5 t}+6 e^{6 t}\right)$

$M^{\prime}(0)=E(X)=\frac{1}{6}(1+2+3+4+5+6)$

$\Rightarrow E(X)=\frac{21}{6}$

$M^{\prime \prime}(t)=\frac{1}{6}\left(e^{t}+4 e^{2 t}+9 e^{3 t}+16 e^{4 t}+25 e^{5 t}+36 e^{6 t}\right)$

$M^{\prime \prime}(0)=E(X)=\frac{1}{6}(1+4+9+16+25+36)$

$\Rightarrow E\left(X^{2}\right)=\frac{91}{6}$

Hence, (a) moment generating function for X is $\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$ .

(b) $\mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}$

6 0

4 years ago

Which steps would prove the circles similar?

Eddi Din [679]

Answer:

You can translate smaller circle onto larger circle so centers line up and then dilate to prove similarity.

Step-by-step explanation:

8 0

3 years ago

Which expression is equivalent to (cd)^(5)

zubka84 [21]

If you would like to find the equivalent expression to (c*d)^5, you can do this using the following steps:

(c*d)^5 = c^5*d^5 = c^5d^5

The correct result would be c^5d^5.

8 0

3 years ago

Read 2 more answers

3/12+ = 7/12 as a faction please help me

ohaa [14]

Answer:

10/12 or simplified its 5/6

Step-by-step explanation:

3+7 = 10

you keep the 12

10÷2 = 5

12÷2=6

common denominator

6 0

4 years ago

On the number line, a bug A is moving in the positive direction from the point 0, and a bug Bis moving in the negative direction

sukhopar [10]

Answer:

$x=st$

$y=-5t$

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

so

The distance is equal to multiply the speed by the time

Let

s ----> the speed in units per second

d ---> the distance in units

t ---> is the time in seconds

BUG A

we have

$d=18\ units$

$t=3\ sec$

The speed is equal to

$s=\frac{d}{t}$

substitute

$s=\frac{18}{3}=6\ units/sec$

If x is the point reached by A after t seconds

then

Multiply the speed by the time

$x=st$

$x=6t$

BUG B

we have

$d=-15\ units$

$t=3\ sec$

The speed is equal to

$s=\frac{d}{t}$

substitute

$s=\frac{15}{3}=5\ units/sec$

If y is the point reached by B after t seconds

then

Multiply the speed by the time

$y=st$

$y=-5t$ ----> is negative because B is moving in the negative direction

3 0

3 years ago

Read 2 more answers