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Mathematics II. (GT_AGMNE013, GT_AKMNE014-17) 2024/2025_2
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Evaluate.P6, 4
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Find the expected value of the random variable in the experiment.Three coins are tossed, and the number of tails is noted.
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Find the probability.Assuming that boy and girl babies are equally likely, find the probability that a family with four children has all boys given that at least one is a boy.
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Find the inverse of the matrix, if it exists.
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Provide an appropriate response.Find the steady state vector for the transition matrix P = 
.Rows represent current states, columns represent next states!
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Provide an appropriate response.A red urn contains 4 red marbles, 2 blue marbles, and 4 green marbles. A blue urn contains 2 red marbles, 2 blue marbles, and 1 green marble. A green urn contains 3 green marbles. A marble is selected from an urn, the color is noted, and the marble is returned to the urn from which it was drawn. The next marble is drawn from the urn whose color is the same as the marble just drawn. Thus, this is a Markov process with three states: draw from the red urn, draw from the blue urn, or draw from the green urn. Write the transition matrix P. Rows represent the first draw, columns represent the second draw!
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Provide an appropriate response.According to data collected during one year in a large metropolitan community, 30% of commuters used public transportation to get to work, and this rose by 4% the following year. This is modeled by the transition matrix 
M = 
S0 = [0.3 0.7]where P represents the percentage of people that use public transportation and P' the percentage of people that do not. What percentage of commuters in this community will use public transportation in the long run?Rows represent current states, columns represent next states!
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Find the expected value of the probability density function to the nearest hundredth.f(x) = 4x-5; [1, ∞)
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Provide an appropriate response.If X is normally distributed with μ = 20 and σ = 4, find P(16 ≤ X ≤ 18).
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Provide an appropriate response.If the density function for the random variable X is f(x) = 
, find k.
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