Toss a fair coin twice. Let X denote the number of tails. Find the probability mass function of X.
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- 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? Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending orderPlease answer.Let X be the total amount saved in dollars at the cash register. The pdf of X is given by: Value of X 8 20 28 40 50 58 70 probability 0.36 0.21 0.24 0.1225 0.0175 0.03 .0175 0.0025 According to the table, what is the chance I save between $16 and $50, exclusive? P( 16 < X < 50 ) = Do not round, express your answer as a proportion using up to 4 decimal places.
- Solve for the mean and variance of the following probability mass function.Let Z be the standard normal random variable. Let X1 = Z, X2 = -Z be independent random variables. Find the probability density function, mean, and variance of X1 + X2The probability density of a random variable X is given in the figure below. From this density, the probability that X > 1.74 or X < 0.06 is:
- Hi, I need some help for this question. I need more explains. Please do not copy chatgpt! Thanks a lot. A bag contains 17 red marbles and 8 blue marbles. A friend reaches in and selects 5 marbles at random, with replacement. For each red marble drawn you win $1; for each blue marble you lose $1. Let W denote your net winnings.(a) Find the probability mass function for W.(b) Calculate the expected value for your net winnings.(c) Now suppose that, instead of drawing the marbles with replacement, your friend now draws 5 marbles without replacement. Find the modified PMF of W, under this new situation.Please provide detailed solution asap for each part pleaseSuppose a single die was rolled. Let x be the random variable representing the number of even numbers occur. Find the probability of each of the values of the of the random variable X. construct the probability mass function.
- An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.02 and fills are independent. Determine the probability mass function of the number of fills (x) before the manufacturing line is stopped.Which of the following is used to represent the Discrete Random Variables? a. Probability Machine Function b. Probability Density Function c. Probability MachineIn a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pas or fail. Assume that the probability that a wafer passes the test is 0.6 and that wafers are independent. Determine the probability mass function of the number of wafers from a lot that pass the test. Round your answers to three decimal places (e.g. 98.765). P(X = 0) = i P(X = 1) = i P(X = 2) = i P(X = 3) = i
