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In a game you flip a coin twice, and

record the number of heads that occur.

You get 10 points for 2 heads, zero

points for 1 head, and 5 points for no

heads. What is the expected value for

the number of points you’ll win per

turn?

record the number of heads that occur.

You get 10 points for 2 heads, zero

points for 1 head, and 5 points for no

heads. What is the expected value for

the number of points you’ll win per

turn?

Answered! |

assume that a tree is randomly distributed in a degraded forest preserve with lambda=40 trees/seedlings per 100 m2 (meter squared). if two 100 m2 (meter squared) plots are randomly chosen then what is the probability that one of the plots has at least 30 trees/seedlings while the other plot has 30 or less such trees? (no continuity correction, hint: use a normal approximation to a poisson).

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A disease is present in 22% of a population and is not present in the remaining

78%. An imperfect clinical test successfully detects the disease and with

probability 0.70. Thus if a person has the disease in the serious form, the

probability is 0.70 that the test will be positive and it is 0.30 if the test is negative.

Moreover among the unaffected persons, the probability that the test will be

positive is 0.05. (5)

(i) A person selected at random from the population is given the test and the

result is positive. What is the probability that the test will be positive is

0.05.

(ii) What is the probability that the test correctly detects cancer?

78%. An imperfect clinical test successfully detects the disease and with

probability 0.70. Thus if a person has the disease in the serious form, the

probability is 0.70 that the test will be positive and it is 0.30 if the test is negative.

Moreover among the unaffected persons, the probability that the test will be

positive is 0.05. (5)

(i) A person selected at random from the population is given the test and the

result is positive. What is the probability that the test will be positive is

0.05.

(ii) What is the probability that the test correctly detects cancer?

Answered! |

A person has to select one of three capsules. one capsule makes his weight increase by 1 kg, another one ensures weight doesn't change. the third one makes him gain 2kg n also compels him to select one of three capsules once again - all similar to d first set of 3 capsules. the person has no way of identifying d capsules beforehand and is equally likely to take any of d three capsules at any stage. find d expected gain in weight.

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company A is determining whether it should submit a bid for a new shopping center. In the past, their main competitor, company B, has submitted bids 90% of the time. if company b does not bid on a job, the probability that company A will get the job is 0.20. if company B bids on job, the probability that company A will the job is 0.15. if company A gets the job, what is the probability that company B did not bid. What is the probability that company A will get the job?

Answered! |

I have seen the demonstration of beta distribution in youtube (https://www.youtube.com/watch?v=3vBBh0SDpqM) at the last B(m,n) is calculated as: (n-1)!(m-1)!/(m+n-1)!.

The question that I ask is:

This last result is obtained for m and n as integers ? if these last ones are réel, what will us obtained for the beta distribution.

I suppose that it will gamma distribution but i'm not sur.

The question that I ask is:

This last result is obtained for m and n as integers ? if these last ones are réel, what will us obtained for the beta distribution.

I suppose that it will gamma distribution but i'm not sur.

Answered! |

The lifetime X of a bulb is a random variable with the probability density function:

f(x)={ 6[0.25-(X-1.5)^2] when 1<=X<=2

f(x)={ 0 Otherwise

X is measured in multiples of 1000 hrs. What is the probability that none of the three

bulbs in a traffic signal have to be replaced in the first 1500 hrs of their operation.

f(x)={ 6[0.25-(X-1.5)^2] when 1<=X<=2

f(x)={ 0 Otherwise

X is measured in multiples of 1000 hrs. What is the probability that none of the three

bulbs in a traffic signal have to be replaced in the first 1500 hrs of their operation.

Answered! |

Car security alarms go off at a mean rate of 4.0 per hour in a large Costco parking lot.

Find the probability that in an hour there will be (Round your answers to 4 decimal places.)

Probability

(a) no alarms

(b) fewer than five alarms

(c) more than seven alarms

Find the probability that in an hour there will be (Round your answers to 4 decimal places.)

Probability

(a) no alarms

(b) fewer than five alarms

(c) more than seven alarms

Answered! |

In a factory turning out of blade, there is a small chance of 1/500 for any blade to be defective. The blades are supplied in a packet of 10. Use poisson distribution to calculate the approximate number of packets containing blades with no defective, one defective, two defectives and three defectives blades in a consignment of 10.000 packets.

In Progress... |

A chartered accountant applies for a job in two firms X and Y. He estimates that the probability of his being selected in firm X is 0.7 and being rejected in Y is 0.5 and the probabilty that atleast one of his applications rejected is 0.6. What is the probability that he will be selected in one of the firms?

Answered! |