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sineoko [7]
3 years ago
12

Can someone PLEASE AND I MEAN PLEASEEE HELP ME plsss i put brainliest !! pleasee

Mathematics
1 answer:
ra1l [238]3 years ago
7 0

Answer:

Step-by-step explanation:

1) y  = 3x + 1

When x = -1 ,   y = 3*(-1) + 1              

                          = -3 + 1

                        y = -2

(-1 , -2)

When x = 0 ,  y = 3*0 + 1

                      y = 1

(0 , 1)

When x = +1 , y = 3*1 + 1

                          = 3 + 1

                       y = 4

(1 , 4 )

Plot these points in the graph and join the points.

2) y = 2x -1

When x = -1 ,         y = 2*(-1) - 1

                                = - 2 - 1

                             y = -3

(-1 , -3)

When x = 0,      y = 2*0 - 1

                        y = -1

(0 , -1)

When x = +1 , y = 2*1 -1

                         = 2 - 1

                       y = 1

(1 , 1)

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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X &gt; 10) b. P(X &gt; 20) c
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(a) The value of P (X > 10) is 0.3679.

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The probability density function of an exponential distribution is:

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(a)

Compute the value of P (X > 10) as follows:

P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353

Thus, the value of P (X > 20) is 0.1353.

(c)

Compute the value of P (X < 30) as follows:

P(X

Thus, the value of P (X < 30) is 0.9502.

(d)

It is given that, P (X < x) = 0.95.

Compute the value of <em>x</em> as follows:

P(X

Take natural log on both sides.

ln(e^{-0.10x})=ln(0.05)\\-0.10x=-2.996\\x=\frac{2.996}{0.10}\\ =29.96\\\approx30

Thus, the value of x is 30.

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