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DochEvi [55]
3 years ago
6

Help with this question please!

Mathematics
1 answer:
vova2212 [387]3 years ago
7 0

<em>V = 120 in^3</em>

<u><em>Here is why:</em></u>

The volume formula for a pyramid is:

V=\frac{1}{3}Bh

The B stands for the area of the base, which in this case is a right triangle. We will find the area of the right triangle first, then plug it into the equation.

The area formula for a triangle is:

A=\frac{1}{2}bh

Plug in the numbers.

A=\frac{1}{2}*9*10

A = 45

Now we have found the area of B, we can plug it into the volume formula for the pyramid.

V=\frac{1}{3}*45*8

V = 120 in^3

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X    |  1        3      5       7

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For this case we have defined the cumulative distribution function like this:

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For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.

f(1) = P(X=1) = P(X \leq 1) - P(X=0) = F(1) -F(0) = 0.4-0=0.4

f(2) = P(X=2) = P(X \leq 2) - P(X=0)- P(X=1) = F(2) -F(1) = 0.4-0.4=0

f(3) = P(X=3) = P(X \leq 3) - P(X=0)- P(X=1) -P(X=2) = F(3) -F(2) = 0.6-0.4=0.2

f(4) = P(X=4) = P(X \leq 4) - P(X=0)- P(X=1) -P(X=2)-P(X=3) = F(4) -F(3) = 0.6-0.6=0

f(5) = P(X=5) = P(X \leq 5) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4) = F(5) -F(4) = 0.8-0.6=0.2

f(6) = P(X=6) = P(X \leq 6) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5) = F(6) -F(5) = 0.8-0.8=0

f(7) = P(X=7) = P(X \leq 7) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5)-P(X=6) = F(7) -F(6) = 1-0.8=0.2

And for any value higher than 7 we have that:

x_i \in [8,9,10,...]

f(x_i) = F(X_i) -F(X_i -1) = 1-1=0

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X    |  1        3      5       7

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Part b

For this case we want to find this probability P(4

And since the random variable is discrete we can write this like that:

P(4

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