CUNTINUOUS DISTRIBUTIONS 145 36 Rock noise in an underground mine occurs at an average rate of three per hour. (See Exercise 65, Chap. 3.) Find the probability that no rock noise will be recorded for at least 30 minutes. 37. California is hit every year by approximately 500 eartiquakes that are large enough to be felt. However, those of destructive magnitude occur, on the av- erage, once a year. Find the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs. (See Exercise 64, Chap. 3.) 38. Consider a chi-squared random variable with 15 degrees of freedom. (a) What is the mean of X²;? What is its variance? (b) What is the expression for the density for X75? (c) What is the expression for the moment generating function for Xs? (d) Use Table IV of App. A to find each of the following: 15 P[X%s< 5.23] P[6.26 22.3] χοι 2 X 95 Section 4.4 39. Use Table V of App. A to find each of the following: (a) P[Z< 1.57]. (c) P[Z = 1.57]. (e) PI-1.25 s (b) P[Z< 1.57]. (d) P[Z>1.57]. (f) Z 10:
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
#38
![CUNTINUOUS DISTRIBUTIONS 145
36 Rock noise in an underground mine occurs at an average rate of three per
hour. (See Exercise 65, Chap. 3.) Find the probability that no rock noise will
be recorded for at least 30 minutes.
37. California is hit every year by approximately 500 eartiquakes that are large
enough to be felt. However, those of destructive magnitude occur, on the av-
erage, once a year. Find the probability that at least 3 months elapse before the
first earthquake of destructive magnitude occurs. (See Exercise 64, Chap. 3.)
38. Consider a chi-squared random variable with 15 degrees of freedom.
(a) What is the mean of X²;? What is its variance?
(b) What is the expression for the density for X75?
(c) What is the expression for the moment generating function for Xs?
(d) Use Table IV of App. A to find each of the following:
15
P[X%s< 5.23] P[6.26 <X}5< 27.5]
X'65
P[X}s>22.3]
χοι
2
X 95
Section 4.4
39. Use Table V of App. A to find each of the following:
(a) P[Z< 1.57].
(c) P[Z = 1.57].
(e) PI-1.25 s
(b) P[Z< 1.57].
(d) P[Z>1.57].
(f) Z 10:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2Fbe614472-c34e-4638-a6b5-a7cb028bc9e9%2Fp934won.jpeg&w=3840&q=75)
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