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3 years ago

Need help with this question

Mathematics

1 answer:

Naddik [55]3 years ago

4 0

Easiest way to graph the line is to connect the intercepts.

-50x - 3y = -1500
-3y = 50x - 1500
y = (-50/3)x + 500
y intercept (0, 500)

-50x - 3(0) = -1500
-50x = -1500
x = 300
(300, 0)

make a line that goes through the points (0, 500) and (300, 0)

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Thetime(inhours)requiredtorepairamachineis an exponentially distributed random variable with parameter λ = 1 . What is 2 (a) the

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Answer:

a) 0.1353

b) 0.3679

Step-by-step explanation:

Let's start by defining the random variable T.

T : ''The time (in hours) required to repair a machine''

T ~ exp (λ)

T ~ exp (1)

The probability density function for the exponential distribution is

(In the equation I replaced λ = L)

$f(x)=Le^{-Lx}$

With L > 0 and x ≥ 0

In this exercise λ = 1 ⇒

$f(x)=e^{-x}$

For a)

$P(T>2)$

$P(T>2)=1-P(T\leq 2)$

$P(T>2)=1-\int\limits^2_0 {e^{-x} } \, dx$

$P(T>2)=1-(-e^{-2}+1)$

$P(T>2)=e^{-2}=0.1353$

For b)

$P(T\geq 10/T>9)$

The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur

$P(T\geq 10/T>9)=P(T\geq 1)$

$P(T\geq 1)=1-P(T$

$P(T\geq 1)=1-(-e^{-1}+1)=e^{-1}=0.3679$

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