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vichka [17]
2 years ago
15

Suppose X has a continuous uniform distribution over the interval [1.3, 6.2]. Round your answers to 3 decimal places.

Mathematics
1 answer:
goldenfox [79]2 years ago
5 0

Answer:

(a) 3.75

(b) 2.00083

(c) 0.4898

Step-by-step explanation:

It is provided that X has a continuous uniform distribution over the interval [1.3, 6.2].

(a)

Compute the mean of X as follows:

\mu_{X}=\frac{a+b}{2}=\frac{1.3+6.2}{2}=3.75

(b)

Compute the variance of X as follows:

\sigm^{2}_{X}=\frac{(b-a)^{2}}{12}=\frac{(6.2-1.3)^{2}}{12}=2.00083

(c)

Compute the value of P(X < 3.7) as follows:

P(X < 3.7)=\int\limits^{3.7}_{1.3}{\frac{1}{6.2-1.3}}\, dx\\\\=\frac{1}{4.9}\times [x]^{3.7}_{1.3}\\\\=\frac{3.7-1.3}{4.9}\\\\\approx 0.4898

Thus, the value of P(X < 3.7)  is 0.4898.

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