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notka56 [123]
3 years ago
11

2 liters of orange juice and 1.5 liters of applejuice

Mathematics
1 answer:
swat323 years ago
7 0
I assume you want the total of liters? 2 plus 1.5 equals 3.5 liters of juice all together :)
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What is the area of the entire triangle if the altitude is a perpendicular
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If y ?-x, and every Xi is i i d with a chi-squared distribution with 14 degrees of freedom, find the MGF of Y M(t) = What is the
Bumek [7]

Answer:

F. chi-squared(df-210)

Step-by-step explanation:

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

We have independent and identically distributed random chi square variables, each one with 14 degrees of freedom X_i \sim \chi^2_{14} for i=1,2,....,15. And let Y the random variable defined as :

Y= \sum_{i=1}^{15}X_i

We have a thorem that says that the distribution of Y is given by: Y\sim \chi^2_{14+14+......+14=15*14=210}

Proof

We need to find first the moment generating function for the random variable Y like this:

M_Y (t) =\prod_{i=1}^{15}M_{X_i (t)}

And the productory is satisfied because we have independent random variables. The moment generating function for a chi square distribution with r1 degrees of freedom is given by:

M_X (t) =(1-2t)^{-\frac{r_1}{2}}

And replacing for each of the 15 distributions we got :

M_Y (t) =\prod_{i=1}^{15}M_{X_i (t)}= (1-2t)^{-\frac{14}{2}} (1-2t)^{-\frac{14}{2}}..... (1-2t)^{-\frac{14}{2}}

And using properties of algebra we got this:

M_Y (t) = (1-2t)^-{\frac{14+14+.....+14}{2}}, t

And we can see that the moment generating function represent a chi square distribution with 14*15=210 degrees of freedom.  

So then the correct option is given by:

F. chi-squared(df-210)

6 0
3 years ago
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