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- Claims 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 a probability density function such as a Normal or bell-shaped curve, the area under the curve is used to make predictions about likelihoods and probabilities. What is the area (use a proportion) under the curve from the lowest possible value to the highest possible value?Benford's law, also known as the first-digit law, represents a probability distribution of the leading significant digits of numerical values in a data set. A leading significant digit is the first occurring non-zero integer in a number. For example, the leading significant digit in the number 127 is 1. Let this leading significant digit be denoted x. Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in the table. 1 3 4 5 7 8 9. P(x) 0.301 | 0.176 | 0.125 | 0.097 0.079 | 0.067 0.058 0.051 | 0.046 Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that behaves according to Benford's law? Please give your answer to the nearest three decimal places.
- Calculate the expected value for this discrete probability distribution: X P(x) 2 0.10 3 0.25 4 0.25 5 0.40 Write you solution to two decimal places.Assume that 12 jurors are randomly selected from a population in which 60% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. Number of Mexican-Americans Probability 0 0 1 0.0003 2 0.0025 3 0.0125 4 0.042 5 0.1009 6 0.1766 7 0.227 8 0.2128 9 0.1419 10 0.0639 11 0.0174 12 0.0022 a) Find the probability of at most 4 Mexican-Americans among 12 jurors. Give answer as a decimal. b) Find the probability of more than 4 Mexican-Americans among 12 jurors. Give answer as a decimal.The figure above shows the probability density function for the random variable x. What is P(3≤x<7)?
- Y is a continuous random variable with the probability density function pictured. what is the mean of y?A bag contains three coins. One coin is two-headed and the other two are normal. A coin is chosen at random from the bag and is tossed twice. Let the random variable X denote the number of heads that will appear. What is the probability mass function of X?The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM company's monthly demand. xUnit Demand f(x)Probability 0 0.10 1,000 0.15 2,000 0.30 3,000 0.30 4,000 0.15 a. Determine the expected number of units demanded per month. b. Each unit produced costs the company $7.00 and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2,000 units?
