1. Construct the probability distribution for each discrete random variable. a. Sum of the outcomes when the two dice are rolled. b. Number of girls in a family with 3 children. c. Product of two numbers taken separately from two boxes containing number 1, 2, 3, and 4.
1. Construct the probability distribution for each discrete random variable. a. Sum of the outcomes when the two dice are rolled. b. Number of girls in a family with 3 children. c. Product of two numbers taken separately from two boxes containing number 1, 2, 3, and 4.
1. Construct the probability distribution for each discrete random variable. a. Sum of the outcomes when the two dice are rolled. b. Number of girls in a family with 3 children. c. Product of two numbers taken separately from two boxes containing number 1, 2, 3, and 4.
1. Construct the probability distribution for each discrete random variable. a. Sum of the outcomes when the two dice are rolled. b. Number of girls in a family with 3 children. c. Product of two numbers taken separately from two boxes containing number 1, 2, 3, and 4. d. Sum of 3 numbers taken separately from 3 jars containing 0, 1, and 2. 2. Suppose Mary has yoga classes 3 days in a week. She attends classes 3 days a week 80% of the time, 2 days 15% of the time, 1 day 4% of the time and is absent for the week 1% of the time. Let X be the number of days Mary is present in a week. a. Construct the probability distribution of X in a tabular form. b. What is the probability the Mary will be absent for at most 2 days? c. Compute the mean and standard deviation of X. 3. Consider drawing 2 balls at random with replacement from a jar containing 2 black balls and 4 white balls. Let X be the number of black balls selected. a. Construct a table giving the probability function of X. b. What is the chance of picking at most 1 black balls? c. What is the chance of picking at least 2 black balls? d. Compute the mean and standard deviation of X. 4. A biased coin with probability of 0.7 for a head (in one toss of the coin) is tossed 5 times. Let X be the number of heads. a. Construct a table giving the probability function of X. b. What is the probability of observing 4 heads? c. What is the probability of observing at least 3 tails? d. What is the probability of observing greater than 2 head? e. Compute the mean and standard deviation of X. 5. A blindfolded marksman finds that on the average, he hits the target 4 times out of 5. If the fires 4 shots, a. Construct a table giving the probability of number of times he hits the target. b. what is the probability of 3 hits? c. what is the probability of more than 2 hits? d. find its mean and standard deviation.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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