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Nikolay [14]
4 years ago
14

the mgf of a random variable x is e^3(e^t-1). Find P[mean - standard deviation squared < X < 1/2( mean + standard deviatio

n squared)], where mean and standard deviation squared are mean and variance of X
Mathematics
1 answer:
postnew [5]4 years ago
8 0
The given MGF is that for a random variable following a Poisson distribution with parameter \lambda=3.

This means \mathbb E(X)=\mathbb V(X)=\lambda, and X has PMF

f_X(x)=\begin{cases}\dfrac{3^xe^{-3}}{x!}&\text{for }x\ge0\\0&\text{otherwise}\end{cases}

So, the desired probability is

\mathbb P\left(\lambda-\lambda^2

This is equivalent to

\displaystyle\sum_{x=0}^2\mathbb P(X=x)=\sum_{x=0}^2\frac{3^x}{x!e^3}=\frac{17}{2e^3}\approx0.4232
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A family plans to have the hardwood floors in their square dining room re-finished, and new baseboards installed. The cost of re
Alexus [3.1K]

Answer:

Dimension of room = 18 foot x 18 foot

Step-by-step explanation:

Let the square room is of side a foot,

The cost of re-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot

Total cost is  $1773.

Cost for re-finishing the hardwood floors = Area x 2.25

Area = a²

Cost for re-finishing the hardwood floors = 2.25 a²

Cost of purchasing and installing the new baseboards = Perimeter x 14.5

Perimeter = 4a

Cost of purchasing and installing the new baseboards = 4a x 14.5 = 58 a

Total cost = Cost for re-finishing the hardwood floors + Cost of purchasing and installing the new baseboards

1773 = 2.25 a² + 58a

2.25 a² + 58a - 1773 = 0

a = 18 or a = -43.77(not possible)

Dimension of room = 18 foot x 18 foot

7 0
4 years ago
Translate this sentence into an equation.
puteri [66]

Answer:

20 + d = 40

Step-by-step explanation:

It gives you 20 so you just say you want to add Donnie's age to equal 40. In math,

and/sum means add +

is means equals =

3 0
3 years ago
Thomas finished the 200-meter race in 25. 7 seconds while Mikah finished in 28. 1 seconds. How much faster did Thomas run the ra
kherson [118]

Thomas finished 2.4 seconds faster than Mikah which has higher speed than Mikah.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Main body:

200-meter race finished by Thomas =  25.7 sec

200-meter race finished by Mikah = 28.1 sec

The difference between their time shows How much faster did Thomas run the race than Mikah.

=28.1 - 25.7

=2.4 seconds

Hence, Thomas finished 2.4 seconds faster than Mikah which has higher speed than Mikah.

To know more about arithmetic click on The link below

brainly.com/question/14753192

#SPJ1

4 0
1 year ago
Is 5x² a term in math​
Eduardwww [97]
Yes it is I believe
5 0
3 years ago
Read 2 more answers
The smith family took three days to drive to Florida. They drove m miles on the first day. On the second day, they drive five mo
irina [24]

Answer: 5m + 20 miles

Step-by-step explanation:

Miles driven on first day = m

On the second day, they drive five more miles than they did on the first day. This will be: = m + 5

On the third day, they drove three times as many miles as they did on the second day. This will be:

= 3(m + 5)

= 3m + 15

Total miles driven will now be:

= m + m+5 + 3m + 15

= 5m + 20

4 0
3 years ago
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