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andre [41]
3 years ago
15

Can someone put an answer for each box plzzzz.

Mathematics
1 answer:
Dahasolnce [82]3 years ago
7 0
We need the drop down options..
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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c
GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(c) The value of P (X < 30) is 0.9502.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0

The value of E (X) is 10.

The parameter λ is:

\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10

(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.

7 0
3 years ago
True or false? a triangle can be circumscribed about a given circle
Sphinxa [80]

Answer:\

The answer to you is:

True

7 0
3 years ago
Solve this quadratic equations: 10k^2-9k+2=0.<br><br> \large k= <br><br> \large k=
Dafna11 [192]
Solve the equation for k by finding a, b, and c of the quadratic then applying the quadratic formula.
Answer =
K= 1/2 , 2/5
4 0
3 years ago
Rise over run, unit rate, constant rate of change, and the variable m all represent slope.
nikklg [1K]

Answer:

True.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Find (2 × 104) − (3 × 103). A) 1.07 × 103 B) 1.07 × 104 C) 1.7 × 103 D) 1.7 × 104
pickupchik [31]
2 \times 10^{4} - 3 \times 10^{3} = 2 \times 10^{4} -0.3 \times 10^{4} = (2.0 -0.3) \times 10^{4} = 1.7 \times 10^{4}

Selection D is appropriate.
4 0
3 years ago
Read 2 more answers
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