TVs are employed out by a rental organization. The time X in months between major

fixes has a remarkable circulation with mean 20 months.

I. Find, to 3 huge figures, the likelihood that a TV recruited out by the

organization won't need a significant fix for in any event long term period.

ii. Track down the middle of X.

iii. The organization consents to substitute any set for which the time between significant fixes

is not exactly M months. In any case, the organization would not like to supplant more than

one set in five such sets. Discover the number worth that ought to be fixed for M.

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A study of families uncovered that 58% of all families eat turkey at occasion suppers, 44% eat ham, and 16% have both turkey and ham to eat at occasion dinners. The graph beneath shows this data.

The issue says that 58% of families eat turkey at occasion suppers, so for what reason does the chart show 42% - what does 42% address?

Discover the likelihood that a haphazardly chosen family eats turkey or ham at occasion dinners.

A public report found that treating individuals suitably for hypertension diminished their general mortality by 20%. Treating individuals satisfactorily for hypertension has been troublesome on the grounds that it is assessed that half of hypertensives don't realize they have hypertension, half of the individuals who do know are insufficiently treated by their doctors, and half who are properly treated neglect to follow this treatment by taking the correct number of pills.

On the off chance that the first half rates were each diminished to 40% by enormous training program, at that point what impact would this change have on the general death rate among genuine hypertensives; that is, would the death rate decline and, assuming this is the case, which level of passings among hypertensives could be forestalled by the schooling program?

In a class of 130 SHS understudies, 41 offers agrarian science, 62 offers business and 31 offer visual workmanship. 16 of these understudies offer both agrarian science and business just and 14 offers both business and visual expressions as it were. Expecting none of the understudies offers every one of the three subjects.

I) what is the likelihood of choosing an understudy indiscriminately from the class who offers neither of the subject

4. An inequality developed by Russian mathematician Chebyshev gives the minimum percentage of values in ANY sample that can be found within some number ( 1) standard deviations from the mean. Let P be the percentage of values within k standard deviations of the mean value. Chebyshevs inequality states that for ANY distribution, P 100 * (1 -1/k)2. (a) For any distribution, what does Chebyshevs inequality say about the percentage of values that are within 2, 3, 5, 10 standard deviations of the mean? (b) For each of the distributions below, determine the percentage of observations within 2 and 3 standard deviations of the mean value. Comment on how these percentages compare to the percentage found using Chebyshevs inequality. i. A standard normal distribution (X ~ N(0,1)) ii. An exponential distribution with A = 2 (X ~ exp(2)) iii. A Poisson distribution with A = 2 X ~Pois(2) iv. A binomial distribution with n = 10 and p = 0.2. X ~ binom(10,0.45)Let X1,..., X10 be independent random variables, uniformly distributed over the unit interval [0, 1]. (a) Estimate P(X1 + . . . + X10 2 7) using the Markov inequality. (b) Repeat part (a) using the Chebyshev inequality. (c) Repeat part (a) using the central limit theorem.1. Assume that X is distributed uniformly over the interval [0, 4]. (a continuous RV) i. Find the mean and variance of X. E[X] = 2, Var [ X] = ii. Use the Chebyshevs inequality to calculate an upper bound on the probability that X is outside the interval [0.5, 3.5]. 16 27 iii. Now use the fact that X is distributed uniformly over the interval [0, 4] to calculate the probability that X is outside the interval [0.5, 3.5]. Is it higher or lower than the answer you got in part ii.? iv. Based on your answers in parts ii. and iii., comment on the usefulness of the Chebyshev inequality. The Chebyshev inequality is very useful for evaluating distributions for which you only know the mean and the variance, but not the actual distribution. If you know the actual distribution you can get a more precise answer. But this is only because you are using additional information.(2) Let N : [0, oo) - Z be (the counting function associated to) a Poisson process of intensity A and fix o E (0, co). Show that t - N(at) is a Poisson process and determine its intensity. Hint: Remember that a Poisson process is the unique process with its marginal distributions