Probability Scores 0.05 2 0.2 4 0.1 5 0.15 6 0.1 7 0.4 9 Find the expected value of the above random variable.

High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?

5 Hypothesis Test It is conjectured that the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o'-lantern at their home is 0.62. Of interest is to test this claim versus the alternative that the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o'-lantern at their home is less than 0.62. A simple random sample of 270 people who went trick-or-treating is selected, and 162 of them also had a pumpkin carved into a jack-o'-lantern at their home (and the other 108 did not). If appropriate, use this information to test if the proportion of all people who went trick-or-treating who also had a pumpkin carved into a jack-o'-lantern at their home is less than 0.62 at the a = .10 level of significance. A simple random sample of 270 people who went trick-or-treating is selected, and 162 of them also had a pumpkin carved into a jack-o'-lantern at their home (and the other 108 did not). use this information to…

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How do I find the expected value and standard deviation

4 students apply to a PhD program.  The program rejects 45% of all applicants.  Students are accepted and rejected independently of each other.  Let the random variable X represent the number out of the 4 students who get rejected into the PhD Program. (Hint: Binomial distribution with n=4, P=45%)   What is the mean of the random variable?  (round your answer to 4 decimal places)

The probability distribution of the random variable X is shown below. X -3 -2 1 5 6 10 P(X=x) 0.019 0.067 0.084 0.056 0.16 0.614 The probability that x is at most 1 is  (blank)

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Probability Scores 0.1 0 0.1 1 0.05 3 0.1 7 0.25 8 0.15 11 0.25 14 Find the expected value of the above random variable.

Discrete random variables and expected values