Statistics and Probability Answers

Let X and Y represent the times to failure, in years, of subsystems A and B, respectively. For instance, X and Y might represent the time to failure of two distinct computers on board an aircraft. Suppose X and Y posses the joint density:

Find the probability that both subsystems survive atmost 2 years

The quality control manager of Textiles Ltd. wants to know the probability of getting a specific number of holes or blemishes in a large continuous roll of cloth. Textiles Ltd. sells rolls that contain 10 000 linear meters of cloth. Based on past experience, they have determined that on average there are 3 holes or blemishes per roll. Calculate the probability that in the next roll of cloth sold there are 4 holes or blemishes present.

In a basin area where oil is likely to be found underneath the surface, there are 3 locations with 3 different types of earth compositions, say C1, C2, & C3. The probabilities for these 3 compositions are 0.5, 0.3, & 0.2 respectively. Further, it has been found from the past experience that after drilling of well at these locations, the probabilities of finding oil is 0.2, 0.4, & 0.3 respectively. Suppose, a well is drilled at a location, & it yields oil, what is the probability that the earth composition was C1?

1.       In a basin area where oil is likely to be found underneath the surface, there are 3 locations with 3 different types of earth compositions, say C1, C2, & C3. The probabilities for these 3 compositions are 0.5, 0.3, & 0.2 respectively. Further, it has been found from the past experience that after drilling of well at these locations, the probabilities of finding oil is 0.2, 0.4, & 0.3 respectively. Suppose, a well is drilled at a location, & it yields oil, what is the probability that the earth composition was C1?

Let X~U(5,21) , calculate the expected value for this uniform distribution.

) Let X and Y represent the times to failure, in years, of subsystems A and B, respectively. For instance, X and Y might represent the time to failure of two distinct computers on board an aircraft. Suppose X and Y posses the joint density:

                  Find the probability that both subsystems survive atmost 2 years. 

Calculate karl pearson's coefficient of correlation from the following data :

X - 105, 120, 95, 150, 130

Y - 100, 115, 110, 135, 115

Faculty weekly salaries for 10 teachers in a certain school were coded by dividing each salary by 100. Find the variance of these salaries if the coded observations are 18, 15, 21, 19, 13, 15, 14, 23, 18 and 16 rupees.

7.the relative strength of the relationship in different samples is most accurately assessed by computing the r² values for the samples. TRUE OR FALSE

direct relationships in a set of data are always stronger than indirect or inverse relationship in a data set. true or false?