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Alexxandr [17]
3 years ago
9

Which expression results from using the distributive property 2(5 + r)

Mathematics
1 answer:
Vinvika [58]3 years ago
7 0
Using the distributive property we know we distribute by multiplying the outside values to those inside of the parentheses

outside values: 2

inside values: 5 and r

now multiply out inside values by the outside values

2x5 = 10

2xr = 2r

now plug these values back in for the inside values and take away the outside value and the parentheses

so 2(5+r) using the distribution property is 10+2r
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(Uniform) Suppose X follows a continuous uniform distribution from 4 to 11. (a) Write down the PDF of X. (b) Find P(X ≤ 7). Roun
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b) P(X\leq 7) = F(7) = \frac{7-4}{11-4}= 0.4286

c) P(5 < X \leq 7)= F(7) -F(5) = \frac{7-4}{7} -\frac{5-4}{7}= 0.2857

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And we can find this probability with this formula from the Bayes theorem:

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Step-by-step explanation:

For this case we assume that the random variable X follows this distribution:

X \sim Unif (a=4, b =11)

Part a

The probability density function is given by the following expression:

f(x) = \frac{1}{b-a} , a \leq x \leq b

f(x)= \frac{1}{11-4}= \frac{1}{7}, 4 \leq x \leq 11

Part b

We want this probability:

P(X \leq 7)

And we can use the cumulative distribution function given by:

F(x) = \frac{x-a}{b-a}= \frac{x-4}{11-4}

And replacing we got:

P(X\leq 7) = F(7) = \frac{7-4}{11-4}= 0.4286

Part c

We want this probability:

P(5 < X \leq 7)

And we can use the CDF again and we have:

P(5 < X \leq 7)= F(7) -F(5) = \frac{7-4}{7} -\frac{5-4}{7}= 0.2857

Part d

We want this conditional probabilty:

P(X >5 | X \leq 7)

And we can find this probability with this formula from the Bayes theorem:

P(X >5 | X \leq 7)= \frac{P(X>5 \cap X \leq 7)}{P(X \leq 7)}= \frac{P(5

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