Answer Happy

Please solve the following Communication Theory
question correctly and step by step
Please show all your solution and show the MATLAB
code
Please do not copy and past any random answer, if given
random wrong answer i will report the solution
thanks for understanding
Expectation When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5. But how can this be? That number isn't even on the die! In probability theory the expectation or expected value is an idealised average that reflects the probability of the possible outcomes of something. In our die example, each of the six numbers has a probability of 1/6thof being rolled. This means that if you roll the die lots and lots of times, you should see a 1 in roughly 1/6th of all the rolls, a 2 in roughly 1/6th of all the rolls, a 3 in roughly 1/6th of all the rolls, and so on. So if you have rolled the die ntimes, then each of the numbers comes up roughly n/6times. The number you get when averaging all the outcomes of the nrolls is therefore roughly equal to (n/6 x 1+n/6x2+n/6x3+n/6 x 4+n/6×5+n/6 x 6) A = n = (1+2+3+4+5+6)/6 = 3.5. The strong law of large numbers says that the larger the number n, the closer the actual average gets to 3.5. The number 3.5 is, in a sense, the average you'd get if you'd rolled the die an infinite number of times. The same idea works more generally. Suppose your die is not fair, so the six numbers don't all have the same probability of coming up. Suppose the probability of a 1 is P1, the probability of a 2 is P2, and so on. The average outcome of a large number nof rolls is then roughly (pin × 1+p₂n x 2 +p³nx3+p₁n x4+psn× 5+p6n × 6) A n = P₁ x 1 +p2 x 2 +p3 × 3+p4×4+ps x 5+p6 x 6. This is the idea behind the general definition of expectation. If a random variable has mpossible outcomes X₁up to Xm, with corresponding probabilities Plup to Pm, then the expected value of the outcome is Question: If you roll a die n times, what is the expected value for the sum of the faces? Write a MATLAB program that finds the expected value of die rolling experiment.