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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. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. 1.
    a) False
    b) False
    c) True
    2. False
    3. True

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. 1.a False
    1.b False
    1.c True
    2. False
    3. True
    4. False
    5. True
    6. False

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

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