Probability

1.Let 𝑋 and 𝑌 be two binomial random variables:
a.If 𝑋 and 𝑌 are independent, then 𝑋+𝑌 is also a binomial random variable
b.If 𝑋 and 𝑌 have the same parameters, 𝑛 and 𝑝 , then 𝑋+𝑌 is a binomial random variable
c.If 𝑋 and 𝑌 have the same parameter 𝑝 , and are independent, then 𝑋+𝑌 is a binomial random variable.
2.Suppose that, 𝐄[𝑋]=0 . Then, 𝑋=0 .
3.Suppose that, 𝐄[𝑋^2]=0 . Then, 𝐏(𝑋=0)=1 .
4.Let 𝑋 be a random variable. Then, 𝐄[𝑋^2]≥𝐄[𝑋]. True or false?
5.Suppose that, 𝑋 is a random variable, taking positive integer values, which satisfies 𝐄[(𝑋−6)^2]=0 . Then, 𝑝𝑋(4)=𝑝𝑋(5) .
6.Suppose that 𝐄[𝑋]≥0 . Then, 𝑋≥0 with probability 1, i.e., 𝐏(𝑋≥0)=1.
True or false?

  1. 👍 0
  2. 👎 0
  3. 👁 492
  1. 1.
    a) False
    b) False
    c) True
    2. False
    3. True

    1. 👍 0
    2. 👎 0

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