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timofeeve [1]
3 years ago
9

Place commas correley in the numbers​

Mathematics
1 answer:
Nana76 [90]3 years ago
3 0

Answer: Where?

Step-by-step explanation:

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PLEASE HELP ! (2/5) -50 POINTS -
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symmetric

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3 years ago
Read 2 more answers
Let X and Y be two independent random variables following beta distributions Beta(120, 2020).
Alla [95]

With X,Y\sim\mathrm{Beta}(120,2020), we have identical PDFs

P(X=x)=\dfrac{x^{119}(1-x)^{2019}}{B(120,2020)}

for 0, and 0 otherwise, where

B(a,b)=\dfrac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}

Since X,Y are independent, the joint PDF is

P(X=x,Y=y)=P(X=x)P(Y=y)=\dfrac{(xy)^{119}((1-x)(1-y))^{2019}}{B(120,2020)^2}

for points (x,y) in the unit square, and 0 otherwise.

1. The distribution is continuous, so P(X=0.5)=\boxed0.

2. X+3 is the region in the x,y plane contained within the unit square and above the line y=\frac{x+3}2. This region is empty, because this line lies above the square altogether, so P(X+3.

3. X>Y is the region in the same square below the line y=x. So we have

P(X>Y)=\displaystyle\int_0^1\int_0^xP(X=x,Y=y)\,\mathrm dy\,\mathrm dx=\boxed{\frac12}

4 0
3 years ago
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