3 Question * The random variable X has the probability density function f(x) given by: 3 x2, |x| < 4; f(x) = }128 0, otherwise. 63 If P(X > a) =, then a is equal to: 128' O 1 None of these 3 O 2
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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.There are 4 quarters and 3 dimes and 1 nickel in a coin pouch. Two coins are selected at random. If X assigns the total value of the coins to each outcome, how many distinct values does X take? Find the probability density function of X?A filling station recieves its supply of gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f(x) = 5*(1-x)4 for 0 less than or equal to x and x less than or equal to 1 and f(x) = 0 otherwise. Find the capacity of its tank so that the probability of its supply being exhausted in a given week is 10%
- The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:f(x) = 8 for 11.975 ≤ x ≤ 12.100andf(x) = 0 elsewhere a. What is the probability that a bottle will be filled with 12.02 or more ounces?b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?c. Quality control accepts production that is within .02 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard?q16- The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is: Select one: a. any value between 1 and 11. b. 0.100. c. 0.091. d. above 11.Consider the random variable X with the uniformdensity having α = 1 and β = 3.(a) Use the result of Example 2 to find the probabilitydensity of Y = |X|.(b) Find the probability density of Z = X4(= Y4).
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