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- where appropriate. 1. Experience has shown that the seeds from a certain variety of orchid have a 75% chance of germinating when planted under normal conditions. Suppose n seeds are planted, and let X be the random variable that counts the number of seeds that germinate. (a) What type of random variable is X? Indicate both the type and the appropriate parameters using the "~" notation. Write down the pmf of X, and do not forget to indicate the range of values that x can take on. X ~ px (x) = = (b) What is the minimum value of n so that the probability of at least five of the seeds germinating is at least 90%?Suppose that f (x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.Let � be a continuous random variable distributed by �(11,1.2), find:A) �(�≥8.89)= Keep your answer in 4 decimal places.B) �(�>11.97)= Keep your answer in 4 decimal places.**Notes: DO NOT round any z-score.
- Let X be a random variable with a uniform distribution over the interval (-10, 4]. Compute P(X > -1.4) [The answer should be a number rounded to five decimal places, don't use symbols such as %) Compute Fx(-0.1). [The answer should be a number rounded to five decimal places, don't use symbols such as %)Suppose that discrete random variable X~uni[1,2,3] A random sample of n=36 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.5, assuming that the sample mean would be measured to the nearest tenth.An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
- It was found that 85% of the students graduated from a technical university are employed within 6 months after graduation. A random sample of 20 graduated students were selected. If X the number of employed students, thus X~B(6,0.85) Select one: O True O FalseIf a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!Let X ~ Uniform(a, b). Find Expected value EX.
- Let X be a random variable with a uniform distribution over the interval [-6,5]. Compute P(X > -0.4) (The answer should be a number rounded to five decimal places, don't use symbols such as % Compute Fx(-2.2). (The answer should be a number rounded to five decimal places, don't use symbols such asFor each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfishAn automobile manufacturer has developed a new type of bumper, which is supposed to absorb impacts with less damage than previous bumpers. The manufacturer has used this bumper in a sequence of 25 controlled crashes against a wall, each at 10 mph, using one of its compact car models. Let X = the number of crashes that result in no visible damage to the automobile. 1.The (parameter/random_variable/statistics/variable) , [variable],[statistics],[random_variable] to be estimated is p. 2. Continuing this question, p the is (percentage/median/average/poportion) of such crushes that result in no damage [alternatively, p = P(no damage in a single crash)]. Select the correct answer from the options inside the (bracket).
