A probability density function for the random variable X is given by pi = kt", where k is a constant. What value must k be if X takes on integer values between 0 and 44? Round your answer to five decimal places. A random variable has CDF given by E={A i=0,1,2 li=3 if A = 0.47r then what is p3 ? Round your answer to two decimal places. \fIn Canada, about 78.33% of women over 40 will develop breast cancer in any given year. A common screening test for cancer is the mammogram, but it is not perfect. In about 61.17% of patients with breast cancer, the test gives a false negative: it indicates a woman does not have breast cancer when she does have breast cancer. Similarly, the test gives a false positive in 63.57% of patients who do not have breast cancer: it indicates these patients have breast cancer when they actually do not. If a randomly selected woman over 40 is tested for breast cancer using a mammogram and the test is positive that is, the test suggests the woman has cancer what is the probability she has breast cancer? Round your answer to five decimal places. About 1 in 1,100 people have IQs over 150. If a subject receives a score of greater than some specified amount, they are considered by the psychologist to have an IQ over 150. But the psychologist's test is not perfect. Although all individuals with IQ over 150 will definitely receive such a score, individuals with IQs less than 150 can also receive such scores about 0.04% of the time due to lucky guessing. Given that a subject in the study is labeled as having an IQ over 150, what is the probability that they actually have an IQ below 150? Round your answer to five decimal places. Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. It is thought that clutch sizes are limited by how effectively parents can incubate their eggs. Suppose that on average, gulls have a 12.9% of laying 1 egg, 9.4% of laying 2 eggs, 12.2% chance of laying 3 eggs, and 65.5% chance of laying 4 eggs. What is the expected value of the number of eggs laid by a random sample of 100 gulls? Round your answer to five decimal places. Most medical tests are not completely accurate. For example, a microscopy test for tuberculosis comes out positive with probability 0.01 when the tested individual doesn't actually have tuberculosis. It comes out negative with probability 0.2 when the tested individual does have tuberculosis. Find the probability a randomly chosen individual will test positive if the proportion of tuberculosis in the population is 0.16. Round your answer to five decimal places. \fA blood test for diabetes gives a positive result with a proportion of 0.3 when an individual has diabetes and a negative result with a proportion of 0.04 when they do not. Approximately a proportion of 0.88 of the population has diabetes. If a randomly chosen citizen tested negative, what is the probability that they actually have diabetes? Round your answer to five decimals. Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents, independently and with probability ,u = 0.698. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises independently with probability ,u. All male children carrying the mutation will develop muscular dystrophy, whereas only females whose X chromosomes both carry the mutation will develop the disease. What is the probability that a child will develop the disease? Round your answer to five decimal places. A probability density function for the random variable X is given by pi = k () , where k is a constant. What r(1-r" ) value must k be if X takes on integer values between 1 and n? Hint: >_p' = 1 -r if 0