1(a). If f (x)=ce−0.2x , if 0≤x≤10 and 0, otherwise Based on your computations below, explain and discuss the various probabilities with respect to the given exponential function. (ii)compute the probabilities (alpha) p(x≥5) (beta) p(x<4) (gamma) p(3≤x≤11)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
1(a). If f (x)=ce−0.2x , if 0≤x≤10 and 0, otherwise
Based on your computations below, explain and discuss the various
probabilities with respect to the given exponential
(ii)compute the probabilities
(alpha) p(x≥5)
(beta) p(x<4)
(gamma) p(3≤x≤11)
b). (b)Using Matlab as a software for simulation, write Matlab statements to compute and display the following expression, given the values a=3.1 ; b=2.2 ; c=7.5 ;d=6.4 ;f=6.7.
(i)x=a?b?/c f?/d (ii)y=d−c/a+b (iii) z=3−2a/b+c/d? (iv)s=2/(1/a+2/b+3/ c+4/d+5/f)
(v)r=3sina/4 +5cosb/6
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