The is a function given by the probability that the random variable X is less than or equal to x, for every value x. a. probability density function =1 b. Probability Density Function C. cumulative distribution function d. all above
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- 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…Let 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 0.35The probability density of a random variable X is given in the figure below. 1 2 From this density, the probability that X is between 0.36 and 1.82 is:
- Required information In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: X 0 1 2 0 0.10 0.17 0.06 y 1 0.11 0.23 0.14 2 0.05 0.08 0.06 Find ux. (Round the final answer to two decimal places.)Part 1 This problem involves selecting books from a shelf. Assume that the shelf holds 6 short stories and 2 novels. A student selects 5 books at random. A random variable X is defined to be the number of novels selected. How many different values are possible for the random variable X? 3 Part 2 Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order. Value of X 0 1 2 ProbabilityThe table below shows a probability density function for the discrete random variable X, the number of misspelled words that an editor finds per page in a novel. What is the probability that X is 0, 1, or 4? Provide the final answer as a fraction.
- 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 FalseRequired information In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: X 0 1 2 0 0.10 0.17 0.06 y 1 0.11 0.23 0.14 2 0.05 0.08 0.06 Find P(X= 1 and Y=0). (Round the final answer to two decimal places.)What value(s) of w will make this discrete probability model illegitimate? A. w > 0.1 B. w = 0.1 C. w < 0.1 D. Both A & C.
- kindly help me with this problem in OTHER DISCRETE PROBABILITY DISTRIBUTIONS follow this formath Given; Required; & Solution thank you!Definition. When the sample space of an experiment is finite, a probability density function for a random variable is a table of all possible values of X and their corresponding probabilities. Remember that random variables assign numbers to each outcome. Each outcome has some probability of occurring. IfXis a random variable, when we write Pr[X= 2], we mean Pr[E], where E is the event consisting of all outcomes to which the random variable eX assigns 2. To further explain this complete the following example. Suppose a fair coin is flipped 3 times. A random variable X assigns the number of heads to each outcome. (a) What are all possible values of X? b) Make a table of each of these values and the probabilities associated with them. Again, this table is called the probability density function of X.( c) Suppose that the random variable Y is 2 times the number of the head plus the number of tails flipped, find the probability density function of Yf or this experiment.