Question 1. REM sleep is the phase of sleep when most active dreaming occurs. The amount of REM sleep during the first four hours of sleep can be described by a random variable T with probability density function 2500 f(t)= 100-1 2500 0 0st≤50 50 ≤t≤100 otherwise where T is measured in minutes. a) Sketch the graph of f(t). b) Determine the cumulative distribution function, F(t), and sketch its graph. c) What is the probability that the amount of REM sleep is less than 35 minutes? d) What is the probability that the amount of REM sleep is between 35 and 80 minutes?

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