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Expected Value of the Bernoulli Distribution | Probability Theory
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How do we derive the mean or expected value of a Bernoulli random variable? We'll be going over that in today's probability theory lesson!
Remember a Bernoulli random variable is a random variable that is equal to 1 (success) with probability p and equal to 0 (failure) with probability 1-p. Thus, the expected value can be found by adding 0*(1-p) and 1*p, because these are the possible outcomes (0 and 1) weighted by their respective probabilities ( (1-p) and p) and added together. This sum is 0 + p = p, thus proving the expected value (or mean, if you prefer) of a Bernoulli random variable with probability of success p is p by definition of expected value!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
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+WRATH OF MATH+
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Remember a Bernoulli random variable is a random variable that is equal to 1 (success) with probability p and equal to 0 (failure) with probability 1-p. Thus, the expected value can be found by adding 0*(1-p) and 1*p, because these are the possible outcomes (0 and 1) weighted by their respective probabilities ( (1-p) and p) and added together. This sum is 0 + p = p, thus proving the expected value (or mean, if you prefer) of a Bernoulli random variable with probability of success p is p by definition of expected value!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
********************************************************************
+WRATH OF MATH+
Follow Wrath of Math on...
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