A random variable X has the following probability function.
(i) Find k
(ii) Find p(0 < x < 5)
(iii) Find p(x ≤ 6)
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Final Answer: 1) k=0.1
2) 0.8
3)0.83
Steps:
1) We know that,
[tex]\sum_{x=1}^{7} P(X=x) = 1 \\ \\ =\ \textgreater \ 0 +k+2k+2k+3k+k^{2}+2k^{2}+7k^{2} + k= 1 \\ \\ =\ \textgreater \ 9k+10k^{2} = 1 \\ \\ =\ \textgreater \ 10k^{2} +9k-1 =0 \\ \\ =\ \textgreater \ (10k-1)(k+1)=0 \\ \\ =\ \textgreater \ k= -1(rejected) \:\: or\:\: k= \frac{1}{10} [/tex]
As P(x) is always non-negative ,so k=1/10
2)
[tex]P(0\ \textless \ x\ \textless \ 5) = P(1) +P(2)+P(3)+P(4) \\ \\ =\ \textgreater \ k+2k+2k+3k = 8k=0.8 [/tex]
3) [tex]P(x \leq 6) = P(0) + P(1)+P(2)+P(3)+P(4)+P(5)+P(6) \\ \\ =\ \textgreater \ 0+k+2k+2k+3k+k^{2}+2k^{2} =8k+3k^{2} \\ \\=\ \textgreater \ 8*0.1+3*(0 .1)^{2} =0.83[/tex]
2) 0.8
3)0.83
Steps:
1) We know that,
[tex]\sum_{x=1}^{7} P(X=x) = 1 \\ \\ =\ \textgreater \ 0 +k+2k+2k+3k+k^{2}+2k^{2}+7k^{2} + k= 1 \\ \\ =\ \textgreater \ 9k+10k^{2} = 1 \\ \\ =\ \textgreater \ 10k^{2} +9k-1 =0 \\ \\ =\ \textgreater \ (10k-1)(k+1)=0 \\ \\ =\ \textgreater \ k= -1(rejected) \:\: or\:\: k= \frac{1}{10} [/tex]
As P(x) is always non-negative ,so k=1/10
2)
[tex]P(0\ \textless \ x\ \textless \ 5) = P(1) +P(2)+P(3)+P(4) \\ \\ =\ \textgreater \ k+2k+2k+3k = 8k=0.8 [/tex]
3) [tex]P(x \leq 6) = P(0) + P(1)+P(2)+P(3)+P(4)+P(5)+P(6) \\ \\ =\ \textgreater \ 0+k+2k+2k+3k+k^{2}+2k^{2} =8k+3k^{2} \\ \\=\ \textgreater \ 8*0.1+3*(0 .1)^{2} =0.83[/tex]
Caira14:
Can u help me with my question
metal 3 reacted with the salt of metal 4. the products were metal 4 and a salt and metal 3 . however metal 4 had no reaction with a salt of metal 3. what can you say about the reactivity of m3 and m4
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