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3 years ago

Pair of fair dice is rolled. What is the probability of each of the following? (Round your answers to three decimal places.)

1 answer:

8 0

we are given with two dice and that we are asked in the problem to find the probability of the following:
a. sum at least 4b. sum at least 6
THe sample space of this problem is
{11, 12, 13, 14, 15, 16, 21,22, 23,24,25,26,31,32,33,34,35,36,41,42,43,44,45,46,51,52,53,54,55,56,61,62,63,64,65,66} a total of 36.a. 33/36 = 11/12b.11/36

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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

3 years ago

A = 1/2bh, where A is the surface area and b is the base, and H is the height.

elena55 [62]

When height turns to 3 times height or 3h

we can replace h with 3h and see what happens

A=1/2b(3h)
A=3/2bh
A=3(1/2bh)
well, the area is trippled

4 0

3 years ago

If RST = NPQ, then rt is congruent to<br> Α. NP<br> B. NQ<br> C. PQ<br> D. Qp

PIT_PIT [208]

NQ
This is because you have to see what R is congruent to (based off the order) and you see N. Then you do the same thing for T and you get Q.

4 0

2 years ago

Read 2 more answers

Which angle is an exterior angle of the triangle?

Alekssandra [29.7K]

Answer:

Step-by-step explanation:

Because it is on the outside

3 0

2 years ago

Read 2 more answers

7a(3b-2c+4) simplify by distributing

luda_lava [24]

To simplify by distribution we proceed as follows;
7a(3b-2c+4)
=7a*3b-2c*7a+4*7a
=21ab-14cb+28a
the answer is:
21ab-14cb+28a

4 0

3 years ago