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:
(b)
Compute the variance of X as follows:
(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](https://tex.z-dn.net/?f=P%28X%20%3C%203.7%29%3D%5Cint%5Climits%5E%7B3.7%7D_%7B1.3%7D%7B%5Cfrac%7B1%7D%7B6.2-1.3%7D%7D%5C%2C%20dx%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B4.9%7D%5Ctimes%20%5Bx%5D%5E%7B3.7%7D_%7B1.3%7D%5C%5C%5C%5C%3D%5Cfrac%7B3.7-1.3%7D%7B4.9%7D%5C%5C%5C%5C%5Capprox%200.4898)
Thus, the value of P(X < 3.7) is 0.4898.
The probability that a black and then a blue marble were chosen is 1/16 if the total number of marbles is 16
<h3>What is probability?</h3>
It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Here data is not given so we are assuming:
Total number of marbles = 6(green) + 2(blue) + 8(black) = 16 marbles
Probability of getting black = 8/16 = 1/2
Probability of getting blue = 2/16 = 1/8
From the product rule:
Probability that a black and then a blue marble = (1/2)(1/8) = 1/16
Thus, the probability that a black and then a blue marble were chosen is 1/16 if the total number of marbles is 16
Learn more about the probability here:
brainly.com/question/11234923
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W - y > h/p
h < (w - y)p
*All you have to do is subtract y from both sides and multiply both sides by p to get the answer, answer is in bold.
