For any number of x, the cumulative distribution function (F(x)) is the probability that the observed value of the X will be at most x.
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observed value of the X will be at most x.
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- The probability distribution for X and Y is shown by the table. Find the marginal distribution function value of X = 1. G(1) = X 2 3 1 0.06 0.10 0.04 2 0.10 0.12 0.13 3 0.15 0.19 0.11 YLet X have an exponential distribution with 0-1. The probability P 6. <5is equal toThe probability density function of the length of a cutting blade is f (x) = 1.25 for 74.6 75.2) c. If the specifications for this process are from 74.7 to 75.3, what proportion of blades meets specifications?
- The table below shows the probability distribution function of the number of accidents (X) occur in a day by taxis belonging to a taxi company. x 0 1 2 3 4 P(X = x) 0.5 0.15 0.05 2k k (a) Find the value of k.(b) Find the expected value and standard deviation of the number of accidents (X) occurring in a day.(c) Assume the net profit ($), Y, of the taxi company in a day is given by Y = 10000 – 4000X. Find theexpected value, variance, and standard deviation of the net profit of the taxi company in a day.(d) What is the maximum profit the company earn in a day? What is the corresponding probability?(e) What is the probability that the company loses money in a day?(f) Find the probability that there are exactly 3 days that the company loses money in a week (7 days).Let X be the number of bathrooms in a randomly selected house for sale in Malibu, California. Suppose X has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution function. x 1 2 3 4 5 6 p(x) .05 .20 .32 .27 .10 .06 F(x) .05 .25 .57 a .94 1 a. What is the value of a? b. Calculate the probability that X < 3. c. Calculate the expected value of X. d. Calculate the variance of X. e. Calculate the expected value of x0.37 <_>f. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that each of the 3 selected houses has exactly 3 bathrooms? g. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that exactly two of the selected houses have exactly 2 bathrooms ? h. Malibu has a water crisis. The town board will solve this crisis by charging a special…The following function is a cumulative distribution function. x < -10 0.1510Let X be the number of visits to the dentist's office for a randomly selected student. Suppose that X has a probability distribution function given by the following table: X P(X= x) 0.15 0.65 Find P(X ≤u) where µ = E(X) is the average number of visits. 0.5 0.15 1 1 0.50 2 0.35Claims for a health company insurance are exponentially distributed. An insurance company offers the subscriber two different types of insurance, class A has a coverage of 1.54. For a random loss, with a probability of 0.640. Class B has a coverage of d. with a probability of 0.512. The value of d is:In an uncertain economy, Americans tend to keep spending down. Let x be the amount of money U.S. individuals spend on groceries monthly. Suppose the probability distribution of x is a uniform distribution from $300 to $400 which is represented by the picture below. f(x) 0.010 0.008 0.006 0.004 0.002 300 320 340 360 380 400 X i (a) What is the probability that a randomly selected individual spends between $315 and $370 on groceries each month? (b) Determine whether the following statement is true or false. The variable, the amount an individual plans to spend on groceries per month, is a numerical (quantitative) variable. True O FalseThe lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is less than 51 min.P(X < 51) =The probability distribution given below represents the projected profit (in thousands of dollars) earned from a business over a year. Profit (x) in thousands of dollars f(x) -100 0.05 -50 0.15 0 0.30 50 0.35 100 0.12 200 0.03 a.) What is the probability that the business will operate at a loss for the year? b.) What is the probability that the business will break even? c.) What is the expected value for profit? Fill out the table below to help you calculate the value.if x 20 Find the following: P(X > 22) =| The cumulative distribution function of X: if x 20 The probability that at least one out of 8 devices of this type will function for at least 29 months:
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