ijfihdsiafbewygfywvgydgfnfd rbc hdr

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TRUONG DAI HOC SV PH <small>1:Ud KY THU </small>

AT

THANH PHO HO CHi MINH

KHOA DAO T~O CHAT LUQNG CAO NHOM KIEN THUC KHOA HQC Cd BAN

Cau I. ( 4.5 diJm)

DE

THI CUCH KY HK III N.A.M HQC <small>2022-2023 </small> Mon:

xAc

_{SU.AT THONG KE UNG}<i>_D"(JNG</i> Ma mon hoc: MATH 132901

De <small>thi c6 </small>2 <small>tra.ng. </small> TMi gian: 90 phut.

<small>D1t<;1c phep Sit c,mg tai li~u. </small>

1. MQt <small>Wp c6 </small>50 <small>sinh vieu trong Jo c6 </small>25 <small>sinh vien h9c h.rc gioi. </small>20 <small>sinh vien h9c it.re kha, con 19-i h9c htc trung blnh. Ch9n ngau nhien mot danh sach g6m 3 sinh vien trong lap. Tinh xac suit trong danh sach nay c6 </small><i><small>it </small></i><small>nh§.t </small>1 <small>sinh vien c6 hQC h1c gioi. </small>

<b>2. </b><small>Hlnh ben chrola so do mf,tch di~n c6 </small>3 <small>n11t </small>l>~t <small>tlit t1,1i cac vj trf </small>1, 2 <small>va </small>3. Cac <small>nllt nay d1rc;ic dong </small>md <small>tv d(mg voi xac suat dong moi 1111t la 0</small>.6 <small>va xac suat md moi nllt </small>la 0.4. <small>:\'eu t~1i dau </small>vao <small>C'i'ta </small>rn1:1-ch <lit-11 _r6_{1 tfo hi}₀_{n, h~}_ty_tfuh_x{_u _s₁₁_at_tfo_hi1₎₁₁₁₁_ity_dH<.J<_·_t_._ru_yi'_".11_clti_u_<la11_ra_.

<b>3</b> <small>Cho bien ngau nhien </small><i>X </i> <small>lien </small>tw <small>r.c'i ham </small>m~t

do

<small>xar. </small>s11M

<i>ro </i>

d1:1-n1;

<i><b>f(x) </b></i>= { <i>;(x </i>-

<b>2)(4 </b>- <b>x) </b> ⁿ<small>eu </small>2 <small>~ </small><i><small>X </small></i><small>~ </small>4, <small>neu </small><i>x </i>> <small>4 ho?,C </small><i>x </i>< <small>2</small>

X,k <small>djnh </small><i>a, </i><small>tinh xac suat </small><i>X </i> <small>nh~n gia trj trong khoang </small>(2.5; 3.5). <small>Tinh xac suat trong nam lan thvc hi~n thi nghi~m c6 </small><i><small>it </small></i><small>nhat mot lan </small><i><small>X </small></i><small>nh~ gia trj trong khoang </small>(2.5; 3.5).

<small>hang </small>la bien ngau nhi<small>en </small><i>X </i> (cldu vj<small>: pl111t) ('() </small>p im ph<small>6</small> lllll <small>vdi </small>tnlll~ <small>bluh fa </small>G phi'it .. <small>Tiuh </small>xac· su

at-1 <small>kh,kh hang den hrc;1t plwc V\l tiep theo phai cha it nhAt </small>3 <small>p11t va khog phi.li cha qa </small>8 <small>ph11t. </small> Cau II. (5.5 diJm)

ti-i.ug. <small>Kliao </small>sa.t <small>ugau nhicn </small>hr<:1ng <small>clic;u t.ii'u t.111.1 </small><i>X </i> <small>va Y ( </small><i>don <small>1ri-: </small>k Wh/th,1:n..11) </i><small>cua mot s6 ho gia dlnh tf,ti Nam Bo trong thang 2 va tha.ng 4 nam nay, girai ta thu dtrc;ic bang s6 li~u sau: </small>

<small>Voi m(rc </small>

y

<small>nghia </small>5%, h<small>ay ki§m dinh gia thuyet cho ding hr<;Jng </small>di~n <small>teu th\t trung blnh ci'1a cc ho gia dlnh t::i,i </small>mien <small>Nam </small>Bo trong than!!; _,_{1 n}_a_m_n_ay_la_c_·_ao_h_on_tronp;_th_ang₂ Gia sfr ri'ing <i><small>X, Y </small></i><small>c6 phan ph6i chufi.. </small>

<b>2. </b><small>Kha.o sat ngau nhien </small>250 <small>gia.ng vien kh6i nganh </small>ki <small>thu~t va </small>280 <small>gia.ng vien </small>

kh6i

<small>nganh kinh t~ t.1:1-i klm </small>v_rr A vf: <small>vi0c co sir rl.1.mp; pftn </small>mr.m <small>ki0.rn t.ra </small>

t5

<small>l<S </small>d1:1-o van <small>Tnrnitin hay khong, t.h1 </small>r6 <small>12 </small>

<small>So hi~: BMl/QT-PDBCL-RDTV </small>

<small>Trang: 1 /2 </small>

nh

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<b>a. Voi </b>t9-i khu v1,tc <i><small>m(tc </small></i>

y

ngliia _A_{c6 sii}_3%_,d1,mg ph§.n m@m Turnitin. _hayso sanh ty 1~ giang vif>11 khoi nganh ki thu~t va khoi nganh kinh te

<b>b. </b>Tlm khofo1g m@rn Turnitin. _tin_c~y_98%_cho_ty₁_~giang vien kh{,i _n_ga_._{nh ki thn~t}

a

vtmg A c6 sfr d\mg ph~n

c. Voi TurniLin _ma.u_vo_et_i_._cho_sa_i_s6_n_e_l_u_amu6n tlm 0.05 lhl di? I~ giiitin c(iy _n_g_vila _enLao _k!tnlti_f_,i_ki11heu? <i>u~ </i>t;;ii Vtlllg _A_c6_St_{dt_mg phAn mem 3. Cho mau gh6p <l i ci.ia hai bien ngau nhien <i>X, Y </i>_nhu_sau:

<i>X </i> <b>₃3 3.5 4 4.5 5.5 </b> ₅ ₆ ₆ <b>_{7.5 7.5}</b>

<i>y </i>

<b>₃₈</b>

<b>40 42 45 50 55 55 60 65 73 77 ₇₉₈₇</b>

Voi

so

lieu tren. _{ta c6}_th~_cl\!<loan gia. tri trung blnh _ci'₁_a_bie_n_ngau_nhi_en<i>_Y</i>khi biet gia trj ciia bien ngau nhien <i>X </i>_b _n_g_h_a_{m h}_6iqui tuyen tfnh Un.re nghi~m _h_ay_khong?_Neu_c6_ha.y_d_._r

<loan gia

tri trung blnh ciia <i>Y </i>khi biet <i>X </i>b~ng 10.

<i>Ghi chti: _Can</i>

<i>bo </i>

<i>coi thi khong _d_uqc_g_iiiithich d€ th:i. </i>

Chufin d§.u ra cua h9c ph§.n ( v~ ki~n <i>th(tc) </i>

N9i dung kiem tra [CDR 2.1]: Sfr d\mg du<;1c giai tfch _t₆_h<;1p_cl_~_{tfnh xar}_su5t_H1eo

quan di~m d6ng _kh_a_n_a_ng

[CDR 2.2]: Si.! di.mg d1c<;1c _{cac co}_n_g_{thu:c tfnh xac}_s_u_fi

t., cl~.c biet. la

xac suat c6 di~u _ki~n

[CDR _2.3]:₁_15,.pdtc<;1c bang phan _ph_oi_xa_._c_sufit_ci'₁_a._bi_e_{n n}_ga_u_nhien

rdi r1;tc. Sir d\mg dtr<;1c _ham_phan_ph6i_{xac su§.t va ham}

<small>m~t </small>d('> xac _Cau_I su§.t _cu.abien ngau nhien lien t~c

[CDR <small>2.4]: </small>Tfnh dinh _dt(c;Jc

<i>k5</i>

<i><small>1 </small></i>v9ng, phttdn_{g sa}_i_,_median_,_morl_ci.i_a bien ngau nhien va each SU'. di;mg cac

s6

d~c trung _n_ay

[CDR <small>2.5]: </small> Sfr di.mg d1t<;1c phan phoi sieu _b_i;>_i_._nhi_tlnk_._Poisson_. chuin va _{m6i lien}

M giira

cac phan ph6i nay

[CDR 2.6]: Tfnh _d11<;1c_{gia trj ci.ia trung}_b_l_nh_mau,

phltong sa_{i m}_a_n

b§.ng may tfnh bo tui

[CDR _2._7]:_Tim_dtrc;Jc₍_gia_tri)_ciia_kho

ang tin c~y cho

t.y

1~, trung

Cau _II

[CDR _2.₈_]_:_Sir_di.mg_dtr<;1_{c cac}_tieu_c_huftn

kiJm c1inh gia thi~t ctJ giai quyet cac l>ai toau li u quau va

ap

<small>d\mg </small><ltt<)c <small>troug </small>t.hi.rc

t6

[CDR 2.9]: Sfr d1,mg d1r<;1c _h_a_{m h}₅ _qui_t_uy~n_tfnh_thi.r_c_nghi~m

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