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4 years ago

Convert this to a decimal then a percent

Mathematics

1 answer:

Ahat [919]4 years ago

4 0

9/27=33.3% repeating 3 = 0.3 repeating 3

18/27= 66.6 repeating 6 = 0.6 repeating 6

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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

How many times longer does it take light from the Sun to reach Neptune than Mercury? Express this number in standard notation. E

stealth61 [152]

9514 1404 393

Answer:

77.6

Step-by-step explanation:

The ratio of light times will be the ratio of distances:

(light time to Neptune) / (light time to Mercury)

= (Neptune distance)/(Mercury distance)

= (27.93×10^8 mi)/(0.3598×10^8 mi) = 27.93/0.3598

≈ 77.6

It takes about 77.6 times as long for light to reach Neptune as it does to reach Mercury.

5 0

3 years ago

Gamestop was selling 5 video games for $102.05 how much was game stop charging per video game?

Marizza181 [45]

Answer:

20.41

Step-by-step explanation:

$102.05÷5

Make sure to tell me if i was right!

6 0

4 years ago

Read 2 more answers

A total of 56 student signed up to play in a flag football league.If each team has 10 student , how many more students will need

Ostrovityanka [42]

4.
56/10= 5 r.6
for another team of ten you need 6+_=10
6+4=10

3 0

3 years ago

Read 2 more answers

2) Justify with proper reasoning: (i) The multiplicative inverse of (-4)^(-2) is 4^2. Pls answer fast...

Alja [10]

Answer:

Below.

Step-by-step explanation:

$-4^{-2}$ = $\frac{1}{-16}$

The multiplicative inverse is basically the opposite reciprocal.

In this case, it is 16

$16 = 4^2$

7 0

3 years ago