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Nikolay [14]
3 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]3 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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Compare and contrast the relative frequency for the whole table in part B with the two-way frequency table given in the activity
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Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.

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3 0
2 years ago
Express a decimal number ( ie 0.768) - process description please - as a rational number (96/125)?
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The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as

1\cdot10^2+2\cdot10^1+3\cdot10^0+4\cdot10^{-1}+5\cdot10^{-2}+6\cdot10^{-3}

10^{-n}=\dfrac1{10^n} for any n, so the above is the same as

100+20+3+\dfrac4{10}+\dfrac5{100}+\dfrac6{1000}=\dfrac{100000+20000+3000+400+50+6}{1000}=\dfrac{123456}{1000}

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Now it's a question of reducing the fraction as much as possible. We have \mathrm{gcd}(768,1000)=8 so

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3 years ago
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